Wenger called the humiliation his team's "worst ever performance in Europe".
And he admitted they have no chance of making the Champions League last eight.
Kevin-Prince Boateng started the rout before two Robinho goals and a Zlatan Ibrahimovic penalty condemned the Gunners to their heaviest European defeat.
Boss Wenger blasted: "It was a shocking result and a shocking performance.
"We made mistake after mistake and were deservedly punished.
"It is a night we will never forget — our worst in Europe by far.
"There was not one moment in the entire 90 minutes when we were in the game.
"We were very poor in attack and in defence and we were never in the game.
"It would not be fair for me to blame the pitch, which was a disaster, because our performance was at the same level.
"We do not live in a dream world and we have to be realistic.
"There may be a statistical chance of two per cent we can still go through but realistically we are out of this competition.
"I can't say I did everything perfectly when we have lost 4-0 but I don't believe we made big tactical mistakes.
"Now there is a danger that a disappointment as big as this will have consequences on our belief for the rest of the season.
"We have a very big game in the FA Cup at Sunderland on Saturday and it's an opportunity to show we have the mental strength and character to respond to such a shocking defeat.
"We have let our ambitions down and all the players are very sad.
"But now we have to stick together and win our next game."
Not even Arsenal legend Thierry Henry could make an impact after being introduced as a substitute at half-time.
As he flies back to New York Red Bulls, the Gunners must now turn their attention to qualifying for the Champions League again next season.
Former Arsenal defender Nigel Winterburn rapped: "The experienced players didn't turn up for the manager and seriously let him down.
"The players should be disgusted with themselves. Confidence has been shot to pieces."
Ex-Gunners skipper Patrick Vieira tweeted: "There was a lack of leadership."
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