The Gunners went into the game at Selhurst Park knowing a point would take them fourth in the Premier League, and ahead of Tottenham, but they failed to deliver.
Palace were worthy winners against them, with Jean-Philippe Mateta and Jordan Ayew both scoring in the first-half.
Arsenal were a little better after the break, but Palace remained in control and wrapped up the win thanks to Wilfried Zaha’s penalty.
“We weren’t at the races today and especially in the first-half,” said Arteta.
“We were late to every ball, we were soft in the duels and we didn’t earn the right to play. And when we did a little bit we were sloppy on the ball.
“We didn’t have any dominance, any sequences of play where we could take some control of the game. We conceded two poor goals as well.
“Overall, it is unacceptable. We put our hands up, me the first one, and apologise. We regroup and tomorrow is a new day and a new opportunity to prepare for the game against Brighton.
“I apologise to our supporters. We didn’t have the presence today or the composure to dominate the situation so that is what I’m most annoyed with.
“Some days you are not there and you are late all the time. They got on top of it and had a good atmosphere and we could not get out.
“When we had the big chances we didn’t score to give ourselves the best chance to get back in the game. First of all we need to put our hands up and get the criticism we deserve. Then we accept it, look ourselves in the mirror and look to the next game. This was not good enough.
“We have to face the challenge and the opportunity is in our hands. We have to be honest with ourselves and support each other.”