The North London side were left frustrated by their Premier League opponents after Wigan scored twice in the opening 10 minutes and managed to clinch a 2-1 win at the Emirates last night.
The French boss was seen initiating a confrontation with the fourth official during the match, and failed to shake hands with Wigan manager Roberto Martinez at the final whistle.
"It is disrespectful to people who pay big money to watch the game," said Wenger. "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."
Arsenal scuppered the opportunity of extending their lead in third place to eight points above Tottenham Hotspur.