Beckham's ankle collapsed under him on the greasy surface in the exhibition match, before the injury was compounded by Sydney midfielder Brendon Santalab sliding into his legs.
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.