Jason Puncheon’s half-volley and Scott Dann’s header put Palace 2-0 up at Goodison Park, before Steven Naismith’s tap-in halved the home side’s deficit.
We wanted to win so much that we stopped being ourselves
Cameron Jerome added a third in the 73rd minute, with Kevin Mirallas netting a late consolation four minutes from full time.
The result left the Toffees fifth in the Premier League table and a point behind Arsenal with four games left to play.
“It’s a real disappointment, a result which is hurtful,” said Martinez. “The first half we were fearful, the way we conceded the first goal shows that.
“They didn’t have the threat to score three goals. We conceded bad goals. The reaction in the second half was ourselves, that was perfect and we were unfortunate not to get something out of the game. But we get ready for the next four games.
“They scored three goals from four shots on target. The breaks went Palace’s way and we congratulate them. They were clinical.
“We wanted to win so much that we stopped being ourselves and that is what we have to learn from.
“We will try and get as many points as we can, it doesn’t change anything.
“We have had a magnificent season and we have incredible potential in this squad.”
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