With less than three minutes on the clock, the Belgian defender's poor clearance from a Rafael cross fell to the feet of Van Persie, who finished in wonderful fashion to open the scoring, with Wenger insisting the mistake was avoidable.
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"The error of Vermaelen is unwelcome. The big defenders don't make these kind of errors," he told Canal+.
"When you give the ball to Van Persie in this situation, two out of three times he scores."
Wenger was also unhappy with the some of the decisions in the game notably the award of a penalty to United and Jack Wilshere's second-half sending off.
The Arsenal manager told Sky Sports: "Yes [Wilshere's sending off] looked harsh from the stand, the second yellow.
"I think we were a bit unlucky, especially with the penalty decision, we always have a penalty against when we play Manchester United, us so we get used to it.
"We had the better chances than but overall in a game like this you ought to not put yourself on the back foot when you are one down."When asked how the he felt when former Arsenal captain Van Persie scored the first goal, Wenger added: "I don't care who scores the goal, you want to win the games. That doesn't matter."