Legendary late-night host David Letterman makes his very first appearance...

Legendary late-night host David Letterman makes his very first appearance on "The Ellen DeGeneres Show" on Thursday.    Credit: Warner Bros./Michael Rozman

Late-night legend David Letterman says he should have ended his network talk show run much sooner.

"Here's the mistake I made: I stayed on television way too long," Letterman, 71, told daytime host Ellen DeGeneres Thursday. DeGeneres, 61, interjected, "That's not true," prompting Letterman to insist, "Yes, it is true, and I'll tell you what happened: It turns out nobody had the guts to fire me," he joked.

Turning serious, the host of NBC's "Late Night with David Letterman" (1982-1993) and CBS' "Late Show with David Letterman" (1993-2015), explained, "I should have left, like, 10 years ago. You want to make sure you have some energy to direct toward other things.” He has since returned to that format with the limited-episode Netflix show "My Next Guest Needs No Introduction with David Letterman," scheduled to begin its second season soon. 

"Now you, nothing but energy," he went on, complimenting DeGeneres, "are doing other things while you're on television. So that's great. I did not. All I cared about was myself. And then the show was gone and so I had to realize, 'Oh, I've been looking through the wrong end of the telescope.' There is more to life than 'So, tell me about your pet beaver,' " he said, offering up a humorous example of one recurring, signature guest bit, "Stupid Pet Tricks."

Letterman also told an anecdote about Mary Connelly, an executive producer for "The Ellen DeGeneres Show" who had worked for 10 years for Letterman. "It was the worst day of my television life and maybe the worst day of my life," he said, recalling that he and Connelly had been throwing a baseball back and forth at his NBC show's Rockefeller Center offices when one hard pitch went through a window on the 14th floor of 30 Rock.

"And down below was Sixth Avenue and the sidewalk," Letterman said, joking, "Well, you know, how many are dead? And I'm stunned, and so I go over to where the window is and I'm just kind of hiding and looking down there, and … people were looking up because shards of glass had rained down on the Avenue of [the] Americas. And I see a guy down there and I can hear him say, 'Hey, look, there's Dave Letterman!' " prompting the late-night host to think, "I'm spending the rest of my life in prison" for having caused someone's death.

"It's a miracle no one got hurt," DeGeneres said. Letterman responded with a jocularly sarcastic look and said, "Good point.”

He added, "So in a situation like that, what do you do? … You send an intern down there! That's what you do!"

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