Wenger slammed his side's defending and also was left frustrated they could not replace Mikel Arteta quick enough when the midfielder hobbled off with an ankle injury which probably rules him out of next week's clash with Chelsea.
Wenger said: "We defended horrendously for the first and second goal. Everybody involved was included for the first and the second goal.
"On top of that we conceded a second goal with 10 men on the pitch. It took us too much time to change and it was absolutely unbelievable.
"After that we had a mountain to climb. I felt in the first half we had enough chances to come back to 2-2, but the second half we dropped our level, we lost our team play, our cohesion and tried too much individually. There was not enough petrol left in the tank anymore.
"We didn't see anyone who could make a difference."
Wenger added: "Chelsea is a massive and vital game for us. We need to recover from the massive disappointment of tonight [Monday] first, then prepare mentally for the next one."
The Gunners boss was, however, less than impressed with Wigan's consistent time wasting - notably from goalkeeper Ali Al Habsi.
"I told the fourth official, 'you know what, he 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," Wenger said.
"It is disrespectful to people who pay big money to watch the game.
"We are sorry we did not play well, but that the referees do not act on that is not right.
"I do not want to look for excuses. I congratulate Wigan, they did well, but I think whether it is tonight or in another game, the referee has to give him a yellow card the second he does it. After you will play football, is it for us or for someone else it is exactly the same."
Wenger added: "Every time the ball goes out on the right, you know the goalkick will go on the left, and he will play short, then do it again.
"I can understand they do it, but it is down to the referee not to allow them to do it."
Roberto Martinez hailed the new-found belief of his Wigan side, who had beaten leaders Manchester United in midweek to build on their win at Liverpool, and were unfortunate not to get something from Chelsea last weekend following controversial decisions.
"We can all be very proud of the manner in which we performed," said the Spaniard, whose side had looked doomed at the turn of the year.
"We always had a mental block against top sides, but we got rid of that at Liverpool and have then felt we can compete against anyone.
"We were very good against Chelsea and deserved a positive result, but it was not a good day in terms of decisions - but nobody can argue we did not deserve the points against Manchester United and Arsenal.
"The second half tonight was as good as we have played this season."
It was a deserved fourth win in five games for Wigan, who have now lost just twice in 11 league matches.
Martinez added: "I always said we would click as a team at the beginning of February, and we had been playing really well but could not win games, which left us a bit frustrated with draws.
"But we have been patient and been able to be stubborn with what we wanted to do and get the results.
"However, we can't really enjoy it because moments like this will mean nothing if we don't get enough points to stay up."