The reigning MLS champions were two goals ahead before conceding three times to a side who ended up with ten men, prompting harsh criticism from Arena, who did opt to take the blame for the nature of the defeat.
"Poor play, a lack of intelligence by our team," Arena said.
"To have a team of players and coaches that are that poor and stupid in the last five minutes of a game, that's my responsibility. It can't be on anybody else but me.
"I'm absolutely embarrassed at that performance. Give our opponent credit, you can't take that away, but our performance is embarrassing. It's disgraceful."
The loss was the Galaxy's seventh of the 2013 season and forced them to fall to fifth place on the Western Conference table.