The reigning MLS champions had held the Red Bulls at bay for almost the entire 90 minutes at The Red Bull Arena on Sunday before Tim Cahill headed home at the death when Cudicini should have come out to meet Juninho's long ball, which infuriated Arena.
"That's not good. That play tonight can't happen," Arena said. "That's 90 percent goalkeeper ball there.
"You saw that goal. We had plays the other way to get a goal, too.
"You have to make a play. They made a play, we didn't - that's the difference in the game. That game should be one point.
"I'm disappointed for our players, because we certainly played well enough to get out of here with a point."