Alexandre Lacazette scored with the last kick of the game to hand Arsenal a home draw after Palace had fought back from a goal down.
Arteta said Arsenal did not convert their goal-scoring opportunities.
"It was more of a collective issue with the lack of composure that we have with the ball in that half," Arteta told reporters.
"We have periods where we suffer and then obviously the areas where we lost the ball, too simply (we) give the ball away and the goals.
"I don't think we were lucky (to get a draw). Well, you could say we were lucky because we scored with the last kick of the game but overall in the game I don't think we were lucky to not lose the game."
Arsenal, who have 11 points from eight games, next host Aston Villa in Saturday's league game.