The Gunners tasted defeat for the first time this season when they went down 2-1 at the Emirates Stadium.
Both goals were preventable, as Fernando Torres outmuscled Laurent Koscielny to hook in Juan Mata's free-kick before the the former Valencia midfielder's second-half delivery was allowed to creep inside the far post after Gervinho had pulled the hosts level just before the break.
Koscielny was kept in the side ahead of 6ft 6ins German Per Mertesacker as captain Thomas Vermaelen returned from illness.
While the France international did not cover himself in glory for either goal, his slight deflection helping Mata's free-kick past Vito Mannone's dive, Arteta insists every one of the Arsenal players must stand up and be counted.
"We have conceded three goals from three set-pieces in the last two games that cost us points and it is not got enough," Arteta said.
"I don't think it is something to do with the defence, it is to do with an individual set-up in the game, which is a free-kick or a corner or whatever, and we haven't defended the ball well enough and we conceded three goals in those two games."
Arteta added: "You cannot blame one player, you have to clear the lines so quickly and you cannot allow runners like that in the box, and it was the same sort of ball for both goals.
"It hurts when you lose points at home against teams like that and you feel you haven't deserved to lose.
"It is frustrating, but I think it was our own fault because we didn't defend those set-pieces."
Arteta, though, insists Arsenal can take confidence from their start to the campaign.
"We have played some of the best teams in the league and we haven't been battered at all. In fact it has been the opposite, we have been better than them through the 90 minutes. I think that is a very positive thing," he said.
"We will bounce back on Wednesday [in the Champions League against Olympiacos]."
Wenger accepts consistency will be the key to Arsenal's chances of mounting a sustained title tilt.
"It is part of human cycle - we are not every day at the same level, and at set-pieces we were poor," he said.
"There was much more in this game for us if we had been more patient and clever.
"When we went in 1-1 at half-time I was convinced we would win the game."
Wenger added: "We will recover from it. It can happen in the season, but they are disappointed because they lost a game they should not have lost."