Barton, who is no stranger to controversy, dropped his shorts in front of home fans after the match in which City defender Micah Richards scored an injury time equaliser to steal a point for the visitors.
Paul Tyrrell, Manchester City club spokesman, was disappointed with the action taken by the FA, and while conceding that Barton has moral responsibilities as a high profile player, he suggested that the midfielder's cheeky actions were only in jest.
"It is deeply disappointing that the Football Association have decided to charge Joey Barton with improper conduct," Tyrrell said.
"The player accepts that some elements of his behaviour following the game with Everton were ill advised and he apologises to anybody who may have felt offended.
"He has been reminded of his responsibilities as a custodian of this football club but we do not believe his actions warrant any further investigation," added Tyrrell.
"We believe the FA should have taken into account the context of the incident and noted he behaved without any malice, and in a light-hearted manner."
Gordon Taylor, Player's Union chief, put his support behind Barton when comparing his indiscretion to that of Tottenham player Didier Zokora in Spurs' match against Portsmouth on the same weekend.
I see a bad moon rising,
I see trouble on the way
Referee Chris Foy awarded a penalty to Tottenham after Zokora appeared to be felled in the box by Portsmouth midfielder Pedro Mendes, however replays showed that there was no contact whatsoever between the players and that Zokora had perhaps conned the referee by blatantly cheating.
"I have to wonder why the FA have chosen to pursue this one, and not the case of Zokora, given that diving is one of the things the game is supposed to be going after," Taylor said in The Daily Mail of the possible charge against Barton.
Merseyside Police were alerted to the incident but have not taken any action against Barton, with Manchester City hoping the FA take the same stance when their disciplinary commission hears the case on Tuesday.