Relegation strugglers Wigan raced into a two-goal lead thanks to efforts from Franco di Santo and Jordi Gomez, before Thomas Vermaelen reduced the deficit.
Wenger, who could see the five-point lead his team hold over North London rivals Tottenham Hotspur reduced to just two points by Saturday evening, insisted that the defeat was not down to lack of concentration.
"It's a shame, it's a defeat that is very difficult to swallow because we have done so well in the last two months. Everybody is deeply disappointed," he told the club's official website.
"I wouldn't put it down to complacency, I just think the way we defended the first two goals was not acceptable. I was still confident at 2-1 especially, but unfortunately in the second half we did not have a lot to offer.
"We have given a lot recently and we were not sharp. We played with [Theo] Walcott, [Alex Oxlade] Chamberlain, [Robin] Van Persie, Gervinho and [Tomas] Rosicky so you couldn't put more strikers on the pitch."
Wigan were reliant on goalkeeper Ali Al Habsi to keep their lead in tact, with the Arsenal front five testing the Omani international on numerous occasions.
And should Arsenal succumb to the same fate as they did against Wigan when they face Chelsea on Saturday, they could find themselves outside the top four should Tottenham and Newcastle United win their games in hand.
Wenger admitted the game now has some added significance following the loss against the Latics.
"Of course, we knew it anyway that the Chelsea game would be massive," said Wenger said. "It is even more important now."
By Dean Mears
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