Arsenal manager Arsene Wenger
The Gunners were out-fought by the home side in every department, leaving their top four hopes in tatters.
Wenger's future has come under renewed scrutiny and the Frenchman says their poor form is a big concern.
He said: "They were sharper than us in many decisive situations. It's not the right moment to analyse. We had a lot of the ball, a lot of possession. We won many second balls as well but in the decisive duels they were stronger, yes.
Alexis Sanchez reacts to Arsenal humiliation against Crystal Palace Mon, April 10, 2017
Click to reveal Alexis Sanchez's reaction to Crystal Palace's second goal against Arsenal
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Click to reveal Alexis Sanchez's reaction to Crystal Palace's second goal
"It's damaging, of course. On that front that is the most difficult for us. It has consequences on our chances to be in the top four.
"You understand that our fans are very unhappy. They came here with the hope they'd win the game.
"Every defeat is a big worry. I've managed over 1,100 games for Arsenal and we're not used to that. It's a big worry. Unfortunately it is like that and we have to respond very quickly and not accept it.
"I'm disappointed and determined to put things right. Tonight the worry is not me, it's the fact we lost a big game and that's a big worry."