David Letterman: 'I don't know why they didn't give my show to a woman'

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David Letterman doesn't miss late-night television at all — as a matter of fact, he "couldn't care less about" it. Also, he thinks CBS should have given his show to a woman.

"I thought for sure I would," the former "Late Show" host told Tom Brokaw when asked if he misses the day part. "And then, the first day of Stephen's [Colbert] show when he went on the air — an energy left me and I felt like, 'You know, that's not my problem anymore.' And I've kind of felt that way ever since."

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"I devoted so much time to the damage of other aspects of my life," Letterman continued. "The concentrated, fixated, focusing on that — it's good now to not have that. I couldn't care less about late-night television."

"I'm happy for the guys — men and women — there should be more women," he added. "And I don't know why they didn't give my show to a woman. That would have been fine. You know, I'm happy for their success. And they're doing things I couldn't do. So that's great."

Later, Brokaw poses the question of if CBS asked Letterman's opinion on who should replace him.

"No. Oh, no. No, they didn't ask me about anything," the bearded comic said. "They were just — they were just happy I was going."

RELATED: David Letterman through the years

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David Letterman: 'I don't know why they didn't give my show to a woman'
David Letterman at reception in NBC's Studio 6A January 19, 1982 at the announcement of new NBC comedy show "Late Night With David Letterman". (AP Photo/Perez)
FILE - In this Feb. 1, 1982 file photo, host David Letterman, right, and guest Bill Murray appear at the taping of the debut of "Late Night with David Letterman" in New York. Murray's 44th and final appearance Tuesday, May 19, 2015, will mark the end of late-night television's most unique and enduring host-guest relationships. After 33 years in late night and 22 years hosting CBS' "Late Show," Letterman will retire on May 20. (AP Photo/Nancy Kaye, File)
David Letterman, host of NBC-TV's "Late Night with David Letterman, " is taken from a tank of water and placed onto a scale in New York while wearing a specially designed suit of sponges, Feb. 14, 1985. Letterman weighed 190 lbs. before and a whopping 500 lbs. after soaking up about 25 gallons of water, during taping for Thursday night's show. (AP Photo/Richard Drew)
Comedian David Letterman shown June 5, 1985. (AP Photo/Wally Fong)
Comedian David Letterman holds his award at the 37th Annual Primetime Emmy Awards ceremony in Pasadena, Ca., Sunday, Sept. 22, 1985. (AP Photo/Nick Ut)
David Letterman in his office at NBC on Jan. 28, 1986 after taping his show. (AP Photo/Mario Suriani)
Performer Paul Simon listens to David Letterman on the set of NBC's "Late Night with David Letterman" in New York, Sept. 11, 1986. Simon was promoting his latest album "Graceland" which features African music. (AP Photo/David Bookstaver)
Farmer Bob Corbett, left, of North Lewisburg, Ohio, shepherds his prize-winning boar named Hog Chief past host David Letterman on the set of NBC's "Late Night with David Letterman" in New York, April 24, 1987. The boar, who had lost of few of his 1,205 pounds when he went on the show, is working to set a world weight record for pigs next August. (AP Photo/G. Paul Burnett)
Bette Davis is a guest of "Late Night With David Letterman" on the set at NBC studios, May 26, 1987. (AP Photo/Ron Frehm)
NBC television's David Letterman, left, guards first base while CBS television's Bob Schieffer, substituting for Dan Rather, keeps one foot planted on the base at New York's Yankee Stadium, Aug. 22, 1987. CBS won the annual challenge between "Late Night With David Letterman" and CBS' "Evening News" with a score of 14-3. (AP Photo/Rick Maiman)
Talk show host David Letterman, center poses with baseball legends Ted Williams, right, and Joe Garagiola, Jan. 1993. (AP Photo)
FILE - In this Jan. 14, 1993 file photo, talk-show host David Letterman announces his move from NBC to CBS at a news conference at CBS Studios in New York. Letterman's show "Late Show with David Letterman," on CBS ran against NBC's "The Tonight Show" with Jay Leno. After 33 years in late night and 22 years hosting CBS' "Late Show," Letterman will retire on May 20. (AP Photo/Alex Brandon, File)
David Letterman, host of NBC's Late Night, speaks during a news conference in New York on July 15, 1993 announcing his move to CBS. Letterman earned an Emmy nomination for best variety, music or comedy series on Thursday, July 22, 1993. (AP Photo/ Alex Brandon)
David Letterman, right, and Bill Murray wave from the side door of the Ed Sullivan Theater in New York on Monday, August 30, 1993. David Letterman brings his late-night lunacy to CBS with guests including comedian-actor Bill Murray and Joel, as well as what the network billed as ?big surprises.? (AP Photo/Jim Cooper)
Television talks show veteran Tom Snyder, left, laughs during an appearance on CBS? ?Late Show with David Letterman,? on Friday, April 22, 1994 in New York. Industry sources have said that Snyder is currently the frontrunner to host the network?s newest talk show that will air at 12:30 a.m., following Letterman?s show. (AP Photo/Alan Singer)
David Letterman is shown during his opening monologue as host of the 67th annual Academy Awards at the Shrine Auditorium in Los Angeles, Ca., Monday, March 27, 1995. (AP Photo/Michael Caulfield)
NEW YORK, UNITED STATES: US Vice President and Democratic presidential candidate Al Gore (R) with talk show host David Letterman 14 September, 2000 after the taping of Letterman's show at the Sullivan Theater in New York City. AFP PHOTO/ Luke FRAZZA (Photo credit should read LUKE FRAZZA/AFP/Getty Images)
NEW YORK, UNITED STATES: Republican presidental candidate and Texas Governor George W. Bush (L) poses for photographers with David Letterman after concluding taping of the 19 October 2000 Late Show with David Letterman in New York. Bush read the Top Ten list poking fun at what he might do if elected. AFP Photo by Paul J. RICHARDS (Photo credit should read PAUL J. RICHARDS/AFP/Getty Images)
BAGHDAD, IRAQ - DECEMBER 24: In this handout photo provided by the U.S. Air Force, 'Late Show' television host David Letterman entertains soldiers at the Coalition Provisional Authority headquarters December 24, 2003 in Baghdad, Iraq. (Photo by Reynaldo Ramon/U.S. Air Force via Getty Images)
Team co-owner David Letterman reacts as one of the team's drivers, Buddy Rice, wins the rain-shortened Indy 500 at Indianapolis Motor Speedway, Sunday, May 30, 2004, in Indianapolis. (AP Photo/Tom Strattman)
Late night talk show host David Letterman salutes "Tonight" show host Johnny Carson during a tribute to the late entertainer during the 57th Annual Primetime Emmy Awards, Sunday, Sept. 18, 2005, in Los Angeles. (AP Photo/Mark J. Terrill)
David Letterman, left, applauds musician Paul McCartney after his performance atop the Ed Sullivan Theater marquee during a taping of "The Late Show with David Letterman" in New York, Wednesday, July 15, 2009. (AP Photo/Charles Sykes)
President Barack Obama is pictured with host David Letterman during a break at a taping of CBS The Late Show with David Letterman, Monday, Sept. 21, 2009, at the Ed Sullivan Theater in New York. (AP Photo/Charles Dharapak)
David Letterman appears onstage at the “The Comedy Awards” presented by Comedy Central in New York, Saturday, March 26, 2011. (AP Photo/Charles Sykes)
Late night talk show host David Letterman speaks at the International Rescue Committee Freedom Award Dinner at The Waldorf Astoria Hotel in New York on Wednesday Nov. 9, 2011. (AP Photo/Eric Reichbaum)
President Barack Obama shakes hands with David Letterman on the set of the "Late Show With David Letterman" at the Ed Sullivan Theater, Tuesday, Sept. 18, 2012, in New York. (AP Photo/Carolyn Kaster)
Ball State University alumnus David Letterman, right, host of CBS's "Late Show," interviews Oprah Winfrey at Ball State University in Muncie, Ind., Monday, Nov. 26, 2012. The conversation is part of the David Letterman Distinguished Professional Lecture and Workshop Series. (AP Photo/Michael Conroy)
NEW YORK, NY - MAY 5: David Letterman films a segment throwing footballs at a moving cab while at Late Show with David Letterman on May 5, 2014 in New York City. Credit: RW/MediaPunch/IPX
In this photo provided by CBS, Serena Williams talks with host David on the set of the “Late Show with David Letterman,” Thursday, Aug. 21, 2014, in New York. Williams will compete in the U.S. Open which begins on Aug. 25. (AP Photo/CBS, John Paul Filo)
NEW YORK, NY - OCTOBER 7: David Letterman seen outside the Ed Sullivan Theater in New York City on October 7, 2014. Credit: RW/MediaPunch/IPX
FILE - In this March 2, 2015 file photo, David Letterman attends "An Evening of SeriousFun Celebrating the Legacy of Paul Newman", hosted by the SeriousFun Children's Network at Avery Fisher Hall in New York. After 33 years hosting late night talk shows, Letterman will retire on May 20. (Photo by Evan Agostini/Invision/AP, File)
NEW YORK - MAY 7: Tina Fey takes off her dress after her last appearance on the CBS Late Show with David Letterman, Thursday May 7, 2015 on the CBS Television Network (Photo by John Paul Filo/CBS via Getty Images)
FILE - In this May 4, 2015 file photo, host David Letterman smiles during a break at a taping of "The Late Show with David Letterman," at the Ed Sullivan Theater in New York. After 33 years in late night and 22 years hosting CBS' "Late Show," Letterman will retire on May 20. (AP Photo/Pablo Martinez Monsivais, File)
A picture of David Letterman hangs outside the Ed Sullivan Theater in New York, Wednesday, May 20, 2015. After 33 years and 6,028 broadcasts of his late-night show, David Letterman is retiring. (AP Photo/Seth Wenig)
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