Yallop had a tough season with the struggling Galaxy, but Beckham believes the coach was not to blame and expressed respect for the fact he was doing what was best for his career.
"But he's not walking away. He's looking after himself, he's looking after his family."
Galaxy forward and USA captain Landon Donovan, who played in both Yallop's title-winning teams in San Jose, joined Beckham in offering his support to Yallop.
Donovan hinted interference from above - perhaps a side-effect of Beckham's arrival - had contributed to the coach's departure.
"I like Frank as a person and I think he's a great coach," Donovan told the Times.
"The unfortunate part is, he hasn't been allowed to show what a good coach he is this year.
"He's not been able to be himself. He's had people in his ear telling him what to do, and he's not been able to just get on with it.
"When he finally was left alone, we went on a seven-game unbeaten streak. I don't think anyone wants to work in those circumstances."