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Wenger is out of contract at the end of the season and has been offered a new two-year deal, although he is yet to announce whether he will continue.
Sixth-placed Arsenal are seven points off the top four with eight games left.
"I've managed over 1,100 games for Arsenal and we're not used to losing like that," said the Frenchman.
"We have to respond very quickly and not accept it."
Some travelling fans told Wenger it was "time to go", also singing "you're not fit to wear the shirt" at the players, as Arsenal were convincingly beaten at relegation-threatened Palace.
Goals from Andros Townsend, Yohan Cabaye and Luka Milivojevic inflicted a fourth straight away league defeat on Arsenal - for the first time during Wenger's 21-season reign.
It leaves the Gunners in serious danger of missing out on a top-four finish for the first time under the 67-year-old.
"I understand our fans are disappointed and we all are deeply disappointed," he said.
"It's very worrying and disappointing the way we lost the game. Palace were sharp, they beat Chelsea the other day, and that shows they have quality.
"We are in a difficult position. The game tonight doesn't help."
Arsenal controlled possession against their 16th-placed hosts, having 72% of the ball, but were unable to make that dominance count.
The Gunners managed just three shots on target, all in the first half.
"That's not Arsenal," said stand-in captain Theo Walcott. "It wasn't us at all.
"All we can do is apologise for that performance.
"Palace just wanted it more. You could sense that from the kick-off.
"We thought we had got out of this little patch and hopefully we haven't been dragged straight back into it. Judging on that performance, it looks like we have."
Arsenal have won only one of their past five Premier League matches, losing three and conceding 11 goals in the process.
Palace boss Sam Allardyce said he had targeted their defensive frailties in the build-up to Monday's game, highlighting the space behind their full-backs for Townsend and Wilfried Zaha to exploit.
"We all know they are in a poor spell of results for the first time for years," said the former England manager.
"The weaknesses with Arsenal have been defensively because they leave Shkodran Mustafi and and Gabriel really exposed.
"Nacho Monreal and Hector Bellerin play like right and left wingers, the wingers come inside with the centre-forward and they're just left on their own."
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Former Blackburn and Chelsea striker Chris Sutton on BBC Radio 5 live:
"At one time, Arsene Wenger managed the Invincibles. He is now managing the Invisibles. He has to go, because the players are not listening.
"The biggest problem with Arsenal is that it's Wenger who makes the decision on his future. I don't get it. It should be up to the owners.
"They must be embarrassed by tonight's performance. It was limp. They were played off the park by a team in danger of relegation.
"It was a pathetic showing."
Arsene Wenger says the uncertainty over his future is not affecting his Arsenal players, but admits their 3-0 defeat at Crystal Palace is "a big worry".