The two late-night talk-show stars discussed the matter Thursday when O'Brien appeared on Letterman's "Late Show" in New York.
O'Brien succeeded Letterman as host of NBC's "Late Night" in 1993 after Letterman left to begin "Late Show" on CBS. Letterman reportedly departed because he was upset NBC gave "The Tonight Show" to Jay Leno when Johnny Carson retired.
O'Brien served as host of "Late Night" until 2009, then briefly became emcee of "The Tonight Show" until January 2010 when NBC forced Leno out of the spot and gave it to O'Brien to keep him from going to a competing network.
O'Brien left NBC when it tried to move the time slot of "Tonight" later to make room for a new show starring Leno.
In November 2010, O'Brien began his late-night cable talk show, "Conan," on TBS.
O'Brien's visit to "Late Show" Thursday was his fifth. He last sat down for an interview with Letterman Jan. 13, 1999.
O'Brien and Letterman commiserated Thursday about their mutual feelings regarding NBC and Leno.
After O'Brien appeared on stage and sat down in the guest chair next to Letterman, the two sat there in a mock awkward silence for a moment or two.
"I think the longer we just sit here, the more uncomfortable it will make Jay," Letterman quipped.
"You know Jay's watching right now," O'Brien said. "You know he's … he's getting a live feed in a satellite truck right now. He's watching every second."
O'Brien imitated Leno's voice, saying as Leno: "Dave looks unhappy. He's gonna pack it in soon."
Letterman then told O'Brien, "I was delighted by everything that happened, except you losing your job."
"I will tell you," O'Brien said, "and this is honest. The only consolation I took during that period was that you were happy."
"What a humanitarian," Letterman laughed.
"I felt ... 'Sometimes Dave seems a tad unhappy in his life, and if this is bringing you some measure of joy, then to hell with my career, you know?'" O'Brien said.
Letterman later said, "And, you know, I refer to that period as 'The Golden Age of Television,' really."
"The period when I lost 'The Tonight Show,' that brief week and a half period, for you, is the golden age of broadcasting?" O'Brien chuckled.