Beckham received a yellow card in the 76th minute after he got into a shoving match with Adrian Serioux and Arturo Alvarez of FC Dallas (2-3-3). Serioux, who brought Beckham down with a slide tackle, was given a red card and ejected.
"It was a terrible tackle. I could have broken my leg," Beckham said. "It's not my decision to give out cards. The player (Serioux) was saying, 'Welcome, baby, welcome,' afterward."
It was Beckham's second yellow card in two Texas appearances, both sellouts. He received one in an exhibition game March 15 after an altercation with FC Dallas midfielder Andre Rocha.
Beckham rejected the notion raised by some that he's been the target of dirty plays in the MLS.
"You either cry about it or get on with it, and it's my motto to get on with it," he said.
Buddle's first goal came in the 31st minute when he dribbled between three defenders before firing a left-footed shot into the left corner of the net from about 18 yards to give the Galaxy (3-3-2) a 2-0 lead.
Los Angeles took a 3-0 lead on an own goal after Donovan's shot from outside the left corner of the penalty box bounced into the net off the leg of FC Dallas captain Duilio Davino.
Chris Klein gave the Galaxy a 1-0 lead in the 25th minute after he fired a shot from 15 yards into the left corner of the goal.
Dominic Oduro scored on a header in the 54th minute from outside the top of the goalie's box for the only FC Dallas goal.