Goals from Leon Osman and Phil Jagielka put the home side in control and despite Arouna Kone pulling one back on 82 minutes, they could not draw level and remain in the relegation zone.
"I'm frustrated and angry. It is a moment of the season where results are starting to be very important," said Martinez.
"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."
Martinez was also angry Wigan were not awarded a penalty after Shaun Maloney went to ground following a challenge from Osman.
"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," added the Spaniard.
"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."