Shaun Maloney appealed in vain for the spot-kick after going down in a challenge from Leon Osman.
Replays suggested Maloney may have been falling before contact from Osman but Latics boss Martinez had no doubt his side, who have now not won in six games, had been hard done to again after also being denied a penalty in last weekend's defeat by Arsenal.
Martinez said: "Shaun Maloney is not a player that looks for penalties. He is someone who once he gets in that one v one situation you know how effective he can be. He goes past his defender easily and there is no need for him to go down but I think if you look at Leon Osman's reaction it tells you everything.
"If you see defending a one v one in the box and someone goes down, you go mad - and rightly so. Leon Osman just went away and showed a face of feeling that he got away with that incident. I don't really understand what the referee saw and I am getting a bit tired of talking about these moments."
A deflected strike from Osman and a Phil Jagielka header, both in the second half, proved enough for the Toffees in a rain-sodden Barclays Premier League encounter despite a late reply from Arouna Kone.
Martinez feels his side must start making the most of every opportunity because decisions and luck continue to go against them. He said: "I'm frustrated and angry. It is a moment of the season where results are starting to be very important.
"We knew we were coming to a difficult place but the way we played the first half, I thought we stopped them from having any momentum.
"We were starting to get into a good position to get a positive result and actions in both boxes cost us. We need to make sure we don't rely on third parties - we don't rely on decisions to get positive results.
"We will learn from it. It is not good enough just to play well in the Premier League, whichever ground you are playing at. If we need to play extra well to get a positive result, that is what we have got to do."