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.
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.
Wenger put the hostile reception down to "disappointed love".
"When he was here he didn't get this kind of reception," said Wenger. "They loved him, so 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."
On the Champions League consequences, Wenger added: "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."
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".
The Arsenal boss also believed the penalty, given when fullback Bacary Sagna brought down Van Persie in the penalty area, was crucial in shaping the course of the game.
Wenger said: "That equaliser played a big part in the game. It put us in a difficult position but overall I can only praise the players for the effort and dynamic and desire we put in. Let's keep it going like that and we'll have a chance to be where we want to be."