He finished the half strongly, scoring from a trademark free-kick from around 25 yards shortly before the break before playing out the full game.
He said: "I was worried at first because I felt as if I'd twisted my ankle again and done the same thing injury I had on the last game of the season with Real Madrid," he said.
"It wasn't as bad - it just caught under the guy that slid in.
"It's all part of the game. It's fine."
Asked why he refused to leave the field, Beckham said: "I always try to stay on whether I'm injured or get kicked in games.
"It's part of the game and I'm quite a stubborn person and when I want to play and when I want to stay on there's not many people who can convince me to come off.
"I was happy to stay on the whole game. I wanted to play.
"So many fans turn out and they expect you to perform and to be out there for as much time as possible."
Galaxy fell 3-0 behind before Beckham and Edson Buddle pulled goals back to make it 3-2.