The last episode of Frasier was broadcast in the US on Thursday, ending the hugely popular comedy's 11 years on television.
Grammer has played the character for a total of 20 years on NBC
The sitcom, based on the life of psychiatrist Frasier Crane, won a record 31 Emmy Awards since it began as a spin-off of TV comedy Cheers.
It went on to match Cheers' 11-season run, with only Dallas series Knots Landing having longer spin-off success.
"I'm proud of it," said actor Kelsey Grammer who played Frasier.
Created by Cheers writers David Angell, Peter Casey and David Lee, the sitcom poked fun at the highbrow neuroses of Frasier Crane and his brother Niles, played by David Hyde Pierce.
"There is an audience for these guys. We proved that. Most of America, frankly, is much smarter than television assumes they are," Grammer said.
Co-writer Peter Casey said the character of Frasier was appealing because "he wasn't a cold intellectual".
"I can't say he never lorded it over people, because there were times that he did," Casey said.
"But deep inside he was a good guy and his motive were usually pretty good."
The show also made stars of John Mahoney, who played their father Martin, Britain's Jane Leeves as Daphne and Peri Gilpin as Frasier's producer Roz.
"I cannot call Frasier a spin-off," said actor David Hyde Pierce.
"I know it is, but it seems to me that, from the beginning, it so stood on its own."
Frasier ended in the US with a two-hour finale, including an hour-long retrospective.
It was not expected to draw the 80.4 million US viewers who tuned in for the last episode of Cheers in 1993, making it the second most-watched TV series finale after MASH.
Nor was it expected to attract the 51.1 million who watched last week's finale of Friends. Nevertheless those who are part of Frasier said it would go out in style.
"I'm very proud of that last episode," co-writer Casey said before the show was broadcast.
"No matter how good the show, they always seem to be waiting in the bulrushes on that final episode. And I just don't see how they're going to get us."
A date has not been set for the UK broadcast of the final episode of Frasier, but a Channel 4 spokesman said it would be shown at the end of June.