The 1-0 defeat at Wembley leaves them seven points behind their fiercest rivals as Tottenham boosted their chances of finishing in the Premier League’s top four.
The Gunners are also six points adrift of Liverpool, who have a game in hand, and Wenger admits missing out on the Champions League for a second consecutive season is a real possibility.
Arsenal missed chances to equalise, but Spurs also missed a host of other chances before Harry Kane popped up to score the winner.
“It will be more difficult to finish in the top four but we have to fight for it,” a rueful Wenger reflected after the game. “The first goal was key and we conceded it.
“Kane made the difference, that’s what he’s about. I have seen the replay, it is no foul, just good centre-forward play. We can only look at ourselves.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.