The Latics boss believes official Kevin Friend is blameless for his side's surrender to the Toffees' fightback, despite being in a commanding position late on in the game
The Latics raced into the lead thanks to an Arouna Kone effort that looked suspiciously offside 10 minutes in, and despite Nikica Jelavic equalising, Wigan regained their lead through Franco Di Santo on 23 minutes. However, Martinez's side were denied all three points by a Leighton Baines penalty three minutes from time.
Despite the result, Martinez remained positive at the outcome, which left his side in 16th place in the table.
"It's always hard to take when you concede really late in the game and you've created the amount of chances we did, but I think it was a tremendous game of football," he told reporters.
"I thought we started better than Everton, the first half probably we were better side. Everton came strong in the second half as you would expect, they played with real tempo and intensity.
"We should have defended better to get the three points. Our disappointment is that the first goal is too soft, you need to defend in a better way in terms of concentration and intensity.
"But I'm pleased with the performance, I felt we performed at a very high level, the way we worked and coped with the intensity of Everton.
"I thought the front three were a joy to watch. We needed a two goal cushion."
Everton ace Marouane Fellaini endured a difficult afternoon, and could have seen red after swinging a leg at Gary Caldwell in the penalty area as well as an aerial challenge on Maynor Figueroa .
"These calls are difficult for referees, but from where I was it looked like he comes across with his arm. But if it's not certain that it's a red card I think it's the right call," Martinez added.
"I thought the referee made the right call, the linesman was in a good position and the fourth official was in a good position so if they decided to give a yellow card I think that's the right decision."