Despite insisting he was "fine with it", Shepard admitted it was an "interesting feeling".
"The only thing I cared about is that you and I were involved," the actor told Hayes.
"Had it been any other thing with a bunch of strangers, I would have been like, 'Oh, whatever. I was at a table read for 45 minutes and then I got fired. Who gives a sh*t?'
"The only (unfortunate) thing is there was no anonymity to it for me. I knew many of the people at that table read. I think maybe that was the only element that I was like, 'Well, that's kind of embarrassing. These are people that I know — and then, I got canned.'"
"I cannot believe they fired you," the Will & Grace star replied.
"It could be as simple as I was terrible at the table read, and that's fine. But that's the only time in being friends (with Hayes) for 12 years where I was like, 'Now I feel like there's something awkward between us.' Because you said to me, 'Oh, my God. I'm so sorry,'" Shepard said.
"I was like, 'Oh, Jesus, you should never be saying (you're) sorry to me in our whole friendship.' You don't ever do anything wrong; you're not the creator of the show."
Will & Grace originally ran from 1998 until 2006, but was revived for new episodes in September last year.
