Galaxy lost on 5-4 penalties to Real Salt Lake after the game ended 1-1 following extra-time.
"We all want to win titles and personally I'd love to be successful," England midfielder Beckham told reporters.
"But I think we have been successful this year without winning tonight, we have quietened a few people along the way which is always nice but we couldn't finish it off."
The Galaxy won the Western Conference title having finished top in qualifying for the play-offs.
Asked whether he was sure he would come back to LA after his loan spell with AC Milan and the World Cup finals next year, if selected for England, Beckham said he would keep his promise.
"Of course, I said I would be back after hopefully the World Cup and that's not going to change," he said.
Beckham had pain-killing injections before the game in order to cope with the effects of a bruised right ankle bone but ended up limping through extra-time with Galaxy having used all three substitutes.
"I had three injections but they wore off after 50 minutes," he said.
"Bone bruising is like that, one of those injuries that doesn't really go away until you rest it and take some time off. So I am just going to have to that in next few weeks," said the midfielder who heads to Italy at the end of December.
COMMITMENT ISSUE
"I'll just rest now. It is the end of the season and I have to just try and rest it and get ready. I'll have rehabilitation because it has been like this for a few weeks," he said.
It would be an easy retort for Beckham to remind critics who questioned his desire of how he played through pain for his team but he said he was no longer interested in debating that issue.
"I've got past that, whether people want to question my commitment, nothing like that is going to make me lose any sleep. If people still want to do it, let them do it," he said.
Beckham, who was coughing badly after the game and has struggled with cold symptoms all week, won praise from Salt Lake skipper Kyle Beckerman for paying a visit to the winning dressing room after the game.
'He's a class act, he really is, you know. I wouldn't expect that from anybody and for him to come in here and just congratulate us... he's just a class act, top drawer and I mean he's done a lot for our league.
"I know it wasn't easy for him to lose this game. He wanted it more than, just as much as everybody else. I'm sure it was tough for him but he came in here and congratulated us and that was big time.'
Beckham said he was impressed with the final held in Seattle, a city where soccer has a strong hold on the sporting public.
"It was a great atmosphere, great city to have a final in. There was a buzz around the city, we knew it would be a good atmosphere and it was."
