Draws for Manchester City and Manchester United in the Premier League earlier on Sunday took them six and five points respectively above Wenger's side, who have a game in hand, in the race for Champions League football next season.
Next weekend Arsenal, who have reached an FA Cup final against league leaders Chelsea, play at home to United and must win to keep up their hopes of a place in the top four.
“It will be very difficult but we have to fight,” Wenger told reporters after Sunday's loss at White Hart Lane. “We have a cup final and the chance to get in the top four.
“We have to give everything in every game. We couldn't afford to lose the game today.
“We have to play more and create more than we did today."
Dele Alli put Spurs ahead after 55 minutes before Harry Kane was fouled in the area soon after and converted the penalty.
Wenger felt the first goal and the spot kick were soft.
Read the full article on eurosport.co.uk: Arsenal manager Wenger refuses to give up on top four