Van Persie looked to have improved the Gunners title aspirations with a 24th minute opener but Robbie Keane, formerly of bitter rivals Tottenham, drew the current leaders level just before the break.
"I am convinced we would have won with 11 players," said the Arsenal boss.
"We took control with 10 men, but imagine what it would have been like with 11?"
"It was very soft," said Wenger of the second booking. "If we get red cards like that from opponents away from home then I'm very happy.
"It was not a red card, it was not a second yellow card. I don't know what it was for and I'm sure he (the referee) doesn't know.
"It's frustrating because we had a nervy first half as we were under pressure to win this game and I knew we would finish very strongly.
"We played high up in the second half and we could not take advantage of the fact we were slowly taking control of the game because we were down to 10 men."