Beckham, 36, set up one goal and won the penalty that provided the other as Galaxy defeated New York Red Bulls 2-1 in the second leg of their play-off.
Arena said: "He helped pick up the team [at 1-0 down]. He was an inspiration."
Galaxy, who won the tie 3-1 on aggregate, face Real Salt Lake in Sunday's final.
That match will be played at the Galaxy's home ground - but serves as an overall semi-final, with the Western Conference champions playing the Eastern Conference winners in the MLS Cup on 20 November.
Sporting Kansas City and Houston Dynamo contest the Eastern final, also in Los Angeles on Sunday.
Galaxy are unbeaten at home this season, having won 13 and drawn five matches.
English striker Luke Rodgers, who played for several lower league teams in England before switching to New York at the start of 2011, opened the scoring for Red Bulls after being played in by former Arsenal forward Thierry Henry.
But Mike Magee nodded in a Beckham corner before half-time and Landon Donovan, who had a loan spell at Everton in 2010, scored from the penalty spot in the second half after Beckham had been fouled.
"His energy in the second half and earning the penalty, it was all David," added Arena.
Beckham, who was substituted with 10 minutes remaining, is yet to decide who he will play for in 2012.
He has spent five years in California with Galaxy but his contract expires at the end of this season.
The club has indicated it may offer the former England midfielder a new deal, while French side Paris Saint-Germain are also interested.
Beckham says he is keen to represent the Great Britain football team at the 2012 Olympics.Watch an extended feature on David Beckham on this week's Football Focus, from 1215 GMT on Saturday.