Wenger’s side are languishing seven points behind third-placed Spurs and five adrift of fourth-placed Chelsea as they paid the price for a mad two minutes at White Hart Lane on Sunday.
Gareth Bale and Aaron Lennon scored for Tottenham while Per Mertesacker pulled on back for Arsenal.
It was the latest setback in a traumatic season for Wenger, who conceded Arsenal have a serious fight on their hands to finish in the top four.
“It will be difficult to come in the top four now as we dropped points we couldn’t afford to drop,” Wenger said.
“I said before the game, we couldn’t drop these points. When you go into a big game like that and are 2-0 down you make it difficult for yourself. It’s a massive challenge but it’s still possible to finish fourth. so we will fight for it,” Wenger said.