The former Chelsea and Tottenham goalkeeper stayed on his line when he should have come out to punch Juninho's floating ball in the 91st minute which was headed into the back of the net by Tim Cahill.
Cudicini was criticised by Galaxy boss Bruce Arena for his mistake and he was quick to take responsibility for the blunder, although he did defend himself, saying a split-second decision was required.
"It was a silly free kick in our half, and from there Juninho played the ball right into the box, and then, of course, I don't know what happened really because they jumped in front of me," Cudicini said. "I tried to reach it, but it was too far.
"It's easy when you're up there. When you're on the pitch, is difficult. I could've done many things. Every time you concede a goal, you can do different things. But, of course, it's disappointing because I don't think we deserved to lose.
"I think we had actually had the better chances, but in the end we go home with zero points."