“The reaction is of disappointment,” Martinez told reporters.
“The result is a hurtful one because of the expectation that we had and the desire that we brought into the game.”
With four games remaining, Everton trail fourth-placed Arsenal by a point but boast a superior goal difference.
Despite potentially tricky games to come against Manchester City and Manchester United, Martinez believes his side can finish in the top four for the first time since 2005.
“We have 12 points to play for, we are close to fourth place and we are still in a good position,” he said.
“I don’t think Arsenal will take maximum points from their remaining games.
“After the weekend (dropping out of the top four) is a disappointment, but if you looked at the start of the season, it’s a magnificent position.”
Goals from Jason Puncheon and Scott Dann put Palace 2-0 up at Goodison Park before substitute Steven Naismith pulled one back for Everton.
Cameron Jerome’s strike restored Palace’s two-goal advantage and despite Kevin Mirallas’ late goal, Martinez was left to rue his side’s first-half performance.
“In the first half we played with a bit of wanting to win so much that we forgot about simple basics,” added the Spaniard.
“In the second half, it was completely different. We were positive and back to being ourselves.
“I felt we were unfortunate not to get a draw after the chances we created.”
“The way we finished the second half gives me great optimism we can finish the season strongly.”
(Reporting By Michael Hann, editing by Ed Osmond)