But former Manchester United trainee John Thorrington scored a 93rd-minute goal for the hosts as they won 1-0 to take the final play-off berth.
The result ends the Galaxy's season, and leaves Beckham facing a long winter before the new campaign gets under way next April.
"I'm a person that likes to train and work every day," said Beckham, who will hope to be involved in England's final Euro 2008 qualifier against Croatia on November 21.
"That's the way it's been through my whole career for the last 15 years. I've never had more than three weeks off in the summer.
"I'm not going to know what to do with myself. I'll be keeping on training and keeping fit no matter what."