The Gunners suffered their latest disappointment of the season on Monday night in the 3-0 defeat at Crystal Palace.
Now seven points behind fourth-placed Manchester City, Wenger acknowledges his team are unlikely to secure a Champions League position.
Wenger, 67, is reported to have been offered a two-year contract extension by Arsenal but has yet to reveal what he intends to do.
"We've recently announced our results from an Arsenal Supporters Trust survey from all our members on the future of Arsene Wenger, and 78 per cent have decided that it is time for Arsene to leave the football club in the summer".
"It will be very hard certainly", said the Frenchman, whose side must still play Tottenham, Manchester United and Everton.
Captain Theo Walcott apologised to fans after Arsenal conceded three goals for a fourth consecutive away league game, and acknowledged: "you could sense from the kickoff that [Palace] wanted it more". "I think the first-half was quite level and then they come out in the second-half stronger than us and we were a bit unfortunate I think on the second goal, and on the third goal it was a penalty that killed our game".
Wenger, who was subjected to chants of "get out of our club" following the defeat, said, "The defeat is damaging, of course, but I'm disappointed and determined to put things right".
"We managed to be strong defensively and to find some opportunities and to score".
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He had led Arsenal to top-four finishes in each of his previous 20 seasons at the helm. But I think we made it easy for them.
Premier League: Crystal Palace 3 (Townsend 17, Cabaye 63, Milivojevic 68-pen) bt Arsenal 0.
The former Bolton and Newcastle manager has now picked up five wins from his last six games, and speaking after the game, he heaped praise on his squad for a well deserved win.
"Tonight the worry is not me, it's the fact we lost a big game and that's a big worry". All we can do is apologise for that performance tonight.
"We thought we had bounced back from that bad patch with the draw against Manchester City and win against West Ham".
"And I've always been a massive admirer - I still am - the class of Wenger the way he speaks after a game, before games".
He continued: "We have to analyse the game".

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