Arsene Wenger's side appeared set to secure qualification for the last 16 of the UEFA Champions League with two games to spare on Tuesday.
Arteta was on target from the penalty spot at Emirates Stadium as the hosts eased into a 3-0 lead against their Belgian opponents, but Anderlecht then came roaring back and capitalised on poor Arsenal defending to secure an unlikely share of the spoils.
While Arsenal are still firmly on course to progress from Group D, their chances of topping the group now look to be slim.
A frustrated Arteta told his club's official website: "We missed a tremendous opportunity.
"You can't afford to make mistakes like this and give any hope to any team in the Champions League because they have the quality to hurt you and that's what happened.
"We need to analyse what we've done because it's not good enough.
"We are too upset [to say anything else], but we have to analyse what happened and it can't happen again."
The Spanish midfielder expects a response when Arsenal visit Swansea City on Sunday.
"That's the best thing in football, we have another game in four or five days against Swansea away, and it needs to be different," he added.
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