Also what is the point in fining a club as rich as chelsea? Its not going to bother themTaken from BBC Sport
The clubs have also been reprimanded by the Football Association after the incident at the Millennium Stadium.
The melee involved players and officials from both clubs and led to three red cards.
The FA's disciplinary commission described the incident as "serious, unacceptable and damaging to the image of the game".
Arsenal duo Emmanuel Adebayor and Kolo Toure and Chelsea's Mikel Jon Obi saw red after 90 minutes of the final, which Chelsea won 2-1.
And the commission concluded Arsenal had been "marginally more involved in the incident, but that Chelsea had past proven cases in recent years regarding the general behaviour of their players where warnings had been issued".
Both teams admitted the charge of failing to ensure their players and/or officials conducted themselves in an orderly fashion and/or refrained from provocative and/or violent behaviour.
The fines follow an FA disciplinary commission hearing.
As well as receiving a three-match ban for his sending off, Arsenal's Emmanuel Adebayor was banned for an additional game and fined £7,500 for his reaction after being shown a red card.
The striker had to be hauled off the pitch after being dismissed for aiming a punch at Chelsea's Frank Lampard.
Arsenal boss Arsene Wenger is facing an FA disrepute hearing after he was charged with improper conduct.
The charges relate to comments Wenger made after the Carling Cup final fracas.
He has been asked to explain his claim "the whole system is not honest", a reference to FA disciplinary rules.
Wenger also suggested the assistant whom referee Howard Webb consulted before sending off Adebayor was a "liar".