Wenger had challenged his side to win all of their remaining games to overhaul Chelsea and Manchester United but defeat at White Hart Lane leaves them six points behind the Blues.
Wenger is not giving up, but he accepts the Gunners' chances are now slim.
He said: "It will be difficult, yes, now of course.
"We'll continue to fight but it makes it very difficult.
"As long as it's not mathematically impossible it is not impossible.
"Our job is to fight and we will do that.
"But even if they drop points we are far (behind)."
The Gunners lost Thomas Vermaelen to a calf strain injury during the game and Wenger estimates the defender will be out for three weeks.
Tottenham captain Ledley King, meanwhile, admitted the 2-1 win was "massive" in his side's bid to claim fourth spot.
Danny Rose opened the scoring with a stunning volley on his full league debut before Gareth Bale doubled the lead just after half-time.
Nicklas Bendtner pulled one back late on but Spurs held on thanks to an inspired performance by goalkeeper Heurelho Gomes.
King told Sky Sports 1: "It's massive. Coming off a disappointing result in the (FA) Cup, it was a good time to play Arsenal.
"We had no time to dwell on that. We knew we had this coming up.
"I've seen the table and it's a big, big result for us.
"It was important we bounced back: we feel we can beat anyone at home."
Gomes said: "It's a good performance for me but it is not the most important.
"When I can make saves like I did today (in every match) then it is most important.
"We played very well. We have a chance (for fourth)."
Harry Redknapp echoed King's sentiments after watching his side go within one point of Manchester City in fourth on the back of Sunday's FA Cup semi-final defeat to Portsmouth.
He said: "It was a great result for us on the back of a big down on Sunday. It knocked us all for six.
"To play like that after Sunday is fantastic.
"The crowd want to beat Arsenal more than anybody. They were right with us tonight.
"We hung in there late on and the keeper made some fantastic saves. He was superb tonight.
"Everybody worked hard and it was a great result."
Redknapp, though, did not feel his side faced undue pressure until late on.
"They started well," he added. "They kept the ball but it was only late in the game the keeper came to our rescue. They had a lot of the ball but they had few clear-cut chances."