Wilshere was handed a second yellow card by referee Mike Dean after a challenge on Evra during the second half, and the France international believes it was an attempt to injure him.
"I think he didn't look for the ball," Evra told reporters.
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The victory sent Sir Alex Ferguson's side top of the Premier League, but Arsene Wenger was unhappy with the referee's handling of the Wilshere situation, arguing that Evra made the most of the situation to get the midfielder sent off.
"Yes, of course," Wenger told reporters when asked if Evra had over-reacted. "He has 10 years in the Premier League.
"I thought the red card was very harsh, and I find the referee very naive.
"When you say to a player: 'For the next foul you're going to get a second yellow', that's a signal to everybody in the opposing team to dive. And of course they do it.
"That is what is absolutely useless. If you get a warning, you are saying to the other team that with the next foul, if you dive, the player is off.
"Why do referees do that? It’s absolutely naive. To me Wilshere's tackle looked a regular challenge.
"If he sends off Wilshere, he has to send off [Robin] van Persie for fouling Bacary Sagna in the second half. From outside, Van Persie's tackle looked a red card."