Arsene Wenger has told Theo Walcott his comments were unacceptable
Arsenal were beaten 3-0 by Palace and lost further ground on the top four.
Afterwards Walcott, who captained the side on the night, claimed Palace had wanted it more.
But Wenger was angered by his remarks.
Theo Walcott said Crystal Palace wanted it more on Monday night
Arsenal lost more ground on the top four with defeat at Selhurst Park
"It is not acceptable," he said.
"But the players were conscious of that when we were in the decisive duels. That's what I said straight after the game. We were beaten, and you have to face reality and respond."
Arsenal face Middlesbrough on Monday night and could find themselves in seventh place and ten points behind fourth spot by kick off.
If they fail to recover it would be the first time Arsenal miss out on the Champions League under Wenger – fuelling the feeling it is time for him to move on.
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And the Frenchman admits Arsenal have a massive task to make up the points in their final eight games.
He said: ”We might get there, we might not get there but the only thing to get there is to believe we can do it.
“That's what we have to focus on; it is not the fear to fail it is the desire to make it and that's the only chance we have to do it.
"It's a big challenge, of course. In football you have to accept that you can win, lose or draw but you have to make sure you perform in the next game and give absolutely everything."