The Latics had led through Paul Scharner's 57th minute header, but the visitors came unstuck as Louis Saha (62) and Leighton Baines (93) scored to snatch victory for the Toffees.
Wigan had chances to claim the win for themselves at the death but it is now three league defeats on the trot.
"I think the players didn't deserve that at all, the performance was fully committed," Martinez told Sky Sports.
"We created enough chances, the hardest thing was to score the first goal and once we had done that and after we hit the post, it should have been game over.
"The way we lost at the end is extremely disappointing because the players don't deserve that at all."
Baines' late winner came from the penalty spot after Emmerson Boyce sent substitute Jo tumbling to the ground and Martinez felt referee Lee Probert over-reacted.
He added: "Well it's a soft penalty - I think it's an emotional decision, but it's not about the decisions of the referee.
"I think overall the performance - probably I'd be disappointed with a draw never mind a defeat."