Van Persie scored from the penalty spot to equalise a second-minute strike from Theo Walcott as Manchester United held Arsenal to a 1-1 draw. With Chelsea beating Swansea it saw the Gunners drop to fourth spot with just three matches remaining.
Wenger said: "If we win our other games it will be enough. I am convinced we will be there (in the top four) but there is no room for dropping points. But the other teams are in the same position."
Arsenal had given champions United a guard of honour on to the Emirates pitch but Van Persie was booed throughout by fans who cheered him during eight years at Arsenal.
"When he was here he didn't get this kind of reception," said Wenger. "They loved him, so today it was a bit disappointed love. He took his penalty very well and I knew when he decided to take the penalty that there was an 80% chance that he would score because he was our penalty taker and I know well that he does that very well. He does many things very well."
Van Persie refused to celebrate converting the spot kick and Wenger revealed his former striker spent some time in the Arsenal dressing room after the match, joking: "Our food is better in our dressing room than their dressing room".
Opposite number Sir Alex Ferguson, meanwhile, saluted Van Persie for staying cool as Arsenal fans tried to unsettle him with volleys of boos.
"He kept his nerve, that was important," said Ferguson. "It was a difficult time for him, the chanting from the fans does not help, but he kept his cool."
Ferguson insisted United were the team looking most to win the game although he admitted Arsenal started strongly in a first half he believed saw referee Phil Dowd have his own problems.
Ferguson said: "I thought the referee found it difficult and the game was running away from him, he found it difficult to control. Once we started getting some momentum going and a bit of heart, we looked like the team to win."
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- Manchester United
- Theo Walcott
- Sir Alex Ferguson