The Spaniard looked aghast on the touchline as a dominant West Ham punished his lacklustre team by scoring three times in the opening 32 minutes with goals by Jesse Lingard, Jarrod Bowen and Tomas Soucek.
Arsenal were in danger of a humiliating drubbing at that point, having failed to get out of first gear, but they hit back in stunning fashion to earn an unlikely point with own goals by Soucek and Craig Dawson and a late Alexandre Lacazette header.
While praising his side's response, Arteta was scathing about the way they started the game.
"This game is going to give me a few nightmares because it is really difficult to stop some of the things we have been doing to hurt ourselves," Arteta said.
He was especially concerned about the way his side were caught napping for West Ham's second goal, when Lingard played a quick free kick to Bowen whose shot evaded keeper Bernd Leno at his near post, and the third goal in which Vladimir Coufal was allowed to cross and Antonio's header was touched in by Soucek.
Even after they had battled back to 3-3 Arsenal almost undid all their good work when Declan Rice ran unopposed half the length of the pitch and forced a save from Leno.
"Hard to explain, we knew the game we would face against West Ham, they can create problems for any team," Arteta said.
"The first goal is something they do really well -- the second and third goal, and the chance that we conceded at the end, is unacceptable."
Despite that, some of Arsenal's attacking play after the break was impressive and rocked West Ham.
"That is the level we can show, the other is top level and probably the best we play all season -- we could have scored six or seven goals and won the game, but we cannot have two faces," Arteta said.
West Ham manager David Moyes said there had been "loads of positives" from his side's display, although he was disappointed that they had missed a chance to move level on points with fourth-placed Chelsea.
"It would have been nice to take the three points because it would have kept us right in there, but we've not lost too much ground," a phlegmatic Moyes said.
"It has been a long time since we finished above Arsenal, we have done our best to make sure they can't catch us. Now we want more, I'm greedy and they are devastated in the dressing room at not taking three points."