The Galaxy conceded goals late in both halves at the Home Depot Center to be beaten 2-1 by the Union and it was a result which clearly miffed Arena whose side have lost their past two matches after a mini-revival of three victories on the trot.
"We gave a game away," Arena said. "That's a game that we should have walked away comfortably with three points in my opinion.
"This is another game where there's nowhere else to look but inside our locker room. We have people in position to get us results and we don't get it done."
Galaxy captain Landon Donovan, who was part of an attack that produced six shots on target and 16 attempts in total, was also rueful of his side's inability to come up with a much-needed win.
"It's frustrating, there's no doubt about it," Donovan said. "It's hard to be too upset because almost everyone played really well but I've been in this game a long time and have seen a lot of games like this where one team dominates and you don't score, and next thing you know you're on the bad end of the result. And that's what happened."