The loss was Arsenal's fourth successive away defeat in the Premier League and left them seven points off fourth.
"They bottle it, they're cowards, they duck out of challenges," was the scathing verdict of former Liverpool defender Jamie Carragher on Sky Sports.
"The best description of the players was two years ago from Graeme Souness, who said they are a team of son-in-laws. But what father would want his daughter to bring one of them home?"
It was Arsenal's fourth successive away defeat in the Premier League and left them seven points off the Champions League places with a game in hand.
Furious away fans taunted Arsenal's misfiring players with chants of "You're not fit to wear the shirt!" and barracked Wenger and his squad as they boarded the team bus after the match.
The back-page headline in The Times, a riff on Palace's nickname, read: "Eagles 3 Butterflies 0."
The Daily Telegraph said the result at Selhurst Park represented "humiliation", while The Sun asked of Wenger: "How can he stay after Selhurst shambles?"
Several newspapers said Arsenal had reached "a new low".
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.
He once again batted away questions about his future after the game, saying he was "not in the mood" to discuss it.
Arsenal great Ian Wright claimed on Twitter that the nature of Arsenal's latest capitulation showed "that dressing room is lost".
Carragher delivered a withering assessment of Arsenal's players, labelling the recent performances of star duo Mesut Ozil and Alexis Sanchez "nothing short of embarrassing".
Former Arsenal striker John Hartson said the defeat against Palace showed Wenger had lost the magic touch that brought him three Premier League titles and four FA Cups in his first nine years at the club.
"I just think now it's time for him to go," Hartson told BBC Radio 5 Live. "It hurts me to say that because I like Arsene Wenger.
"Last night (Monday), you would call that performance inept. There was a lack of leadership, lack of togetherness. The players are playing as individuals. They don't look like a team."