Beckham, who missed the first half of the MLS season while he played for AC Milan, was abused and taunted in his first game back in the US, a July friendly for the Galaxy against the Italian team.
The England midfielder's return also coincided with claims in a book that he had fallen out with Galaxy favourite Landon Donovan and for a moment it seemed the entire season could turn into a circus.
"The reason it didn't happen is because of the way David played and the way he demonstrated that he cares about the LA Galaxy," Arena said in a teleconference on Tuesday.
"His performances quietened his detractors and I think, obviously at the Milan exhibition there were some frustrated fans ... but I never felt that David wouldn't be able to handle it," he added.
"David has been through an awful lot in his career, he has played with some of the biggest clubs in the world and been through a lot of adversity as a player.
"I think he was obviously well prepared to deal with any kind of issues that he was confronted with when he returned and lets face it he has done a wonderful job with that."
The Galaxy came through the playoffs with wins over Chivas USA and the Houston Dynamo and will now face Real Salt Lake in Sunday's final in Seattle.
If the Galaxy win the title, Beckham would have completed a hat-trick of championship wins in England, Spain and the U.S.
Arena said that it helped the reintegration of Beckham into the Galaxy team that the side had begun to gel as a unit prior to his return.
"I think by the time David showed up, we had really established ourselves as a team in the locker-room and whether it was David or any other player coming in they had to step in and contribute.
"David wasn't treated any differently than anyone else - he was accepted for his efforts on the field and he was expected to perform and live up to all his responsibilities as with all the other players.
"David never has a problem with that, he has been a great professional wherever he has been and it only made sense to me that we would get the same kind of effort from him when he returned to LA from Milan and that was the case.
"He has won over his team-mates, won over the supporters and we are really happy for David that 2009 has been a good year for the Galaxy."
