Arena angry with careless Galaxy
Arena's men won the 2011 MLS title but have made a stuttering start to the 2012 season, losing eight of their first 13 league fixtures.
A run of three successive wins appeared to have the Galaxy back on track but they threw away a 3-1 lead in front of over 50,000 fans at Stanford Stadium in California to slip to another defeat.
"We did a poor job today," Arena said.
"The defending on set pieces wasn't good and it cost us the game."
Arena went onto criticise referee Hilario Grajeda for his performance in the match.
"I don't think the officiating was good, there were a couple of handballs in the penalty area that were missed. He (Grajeda) did a poor job managing the game," he said.
"The reason why we had a disturbance at the end of the game was he wasn't in control, I think. There are two competitive teams and things boiled over.
"But the management of the game by the referee was atrocious. But we have no-one to blame, we should not lose that game."
The result capped off a poor week for English midfielder David Beckham, who was surprisingly left out of his country's squad for the Olympics on Thursday.
Beckham did score a free-kick on the half-hour mark but it did not affect the result, as Victor Bernardez, Sam Cronin and Chris Wondolowski scored in a 16-minute period before and after half-time for the winners.
"If you helped the Olympics in your country and don't get named in the team you'd be frustrated, so I'm sure he is," Beckham's teammate, Landon Donovan, said after the loss which he described as 'frustrating'.
Los Angeles - who sit outside the playoff places - will need to bounce back quickly as they prepare to host Philadelphia Union on Wednesday.
San Jose coach Frank Yallop was delighted a bumper crowd were able to see his team fight back to take all three points off the reigning champions.
"It's a wonderful experience, not only for the players, but for the club," he said.
"We've proved that we can sell soccer tickets to a very good event. My phone didn't stop ringing for the last week and we could have had 80,000 here to be honest.
"But what it says is that it's a great market and that people want to see our team. They want to see great players that Galaxy have, like David Beckham, Landon Donovan and Robbie Keane. It bodes well for our future, our new stadium and moving forward with the club."