The Toffees, who had won seven Premier League fixtures on the trot, were beaten at home by a determined Eagles side which now finds themselves sitting 11th.
Jason Puncheon’s 23rd-minute effort and Scott Dann’s goal early in the second half had given Palace a two-goal advantage before Everton substitute Steven Naismith pulled one back just after the hour-mark.
Cameron Jerome then restored the visitors’ two-goal lead prior to an 86th-minute Kevin Mirallas finish which came too late for the home team.
"Defensively to concede three goals you'd expect the opposition to have more chances and more threat," he told Sky Sports.
"I did feel that the first half we had a little bit of a fearful look about our performance, we weren't ourselves at all.
"I think the reaction in the second half was terrific - it deserved something positive out of the game.
"And we created enough chances to do that, bearing in mind that Crystal Palace will always limit you to very little in front of goal because that's the way they are drilled and defensively they've got a terrific record.
"But I just feel that scoring two goals (to get back level) was the hardest part of this game.
"The disappointment is conceding three when they had four shots on target and that's down to probably our feeling of having something to lose today."
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