The Gunners found themselves two goals down inside the first ten minutes thanks to strikes from Franco di Santo and Jordi Gomez. From that moment on, despite Thomas Vermaelen halving the deficit, Wenger felt Wigan spent the remaining 80 minutes running down the clock.
Goalkeeper Ali Al-Habsi was booked for time-wasting in injury-time, but in general play Wigan created the clearer-cut opportunities in an impressive display that leaves them five points clear of the relegation zone.
Frustration was evident in the Arsenal camp at the final whistle, with Wenger failing to shake Martinez's hand while Robin van Persie squared up to Gary Caldwell. And Wenger insists the game was not played in the right spirit by the visitors.
"It is disrespectful to people who pay big money to watch the game," Wenger said.
"I told the fourth official, 'You know what, their goalkeeper will do it all game because he did it after 10 minutes and, with three minutes to go, he will get a yellow card'. That is exactly what happened.
"We are sorry we did not play well - but that the referees do not act on it is not right.
"I do not want to look for excuses. I congratulate Wigan, they did well, but whether it's tonight or in another game, the referee has to act."