If Chelsea take at least nine points from their last four games, they will finish on 74 points. If Tottenham win their four remaining games, they would also finish on 74 points.
However, even if Arsenal won their remaining games against relegated Queens Park Rangers, Wigan Athletic and Newcastle United, they would finish on 73 points and could miss out on a place in the Champions League for the first time in 16 years.
Asked whether the point would be enough for Champions League qualification for a 16th successive season, Wenger replied: "If we win all our games it will be enough and I am convinced we will be there. We will be where we want to be at the end, I am sure of that.
"But you know there is no room for dropping points. We know that."
Arsenal slipped from third to fourth in the table after Chelsea's 2-0 home win over Swansea City on Sunday, while Tottenham Hotspur remained fifth after a 2-2 draw at Wigan Athletic on Saturday.
Arsenal fans booed their former favourite despite Wenger's plea for him to be treated with respect.
"When he was here he didn't get that kind of reception," the Frenchman added. "They loved him - today it was a bit of disappointed love."
Wenger also laughed off Van Persie's goal, saying: "He scored a penalty but it is not completely the same as scoring.
"He takes penalties very well and when he decided to take the penalty I knew there was an 80 percent chance he would score.
"Robin van Persie does a lot of things very well."
