The Gunners went up early through Pierre-Emerick Aubameyang, but Palace responded with two second-half goals.
Alexandre Lacazette salvaged a point for the home side with a 95th minute equaliser.
Speaking after the match, Arteta said: "We managed to score the goal, and we were in control. And then our level dropped.
"We had no composure on the ball, we started to give the ball away too easily, we didn't have any sequences in our passes, we wanted to attack in one or two passes and the distances were too big.
"I think we put the handbrake on a little bit. We started to defend something. We were not moving fluently enough and taking the right decisions, playing forward more and being more ambitious to score the second goal in that moment."
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