The French head coach is coming under untolerable pressure at the north London club following a disastrous run of results.
Arsenal lost 3-0 to Manchester City in the League Cup final at Wembley last weekend following goals from Sergio Aguero, Vincent Kompany and David Silva last term.
The Gunners welcomed the Premier League leaders to the Emirates Stadium on Thursday night to provide Arsenal with an immediate chance to bounce back.
However, the Citizens eased to a resounding 3-0 win in north London courtesy of first-half goals from Bernardo Silva, David Silva and Leroy Sane.
Wenger’s side are in sixth place in the Premier League table and 10 points adrift of fourth-placed Tottenham Hotspur with 10 games to go.
Arsenal have lost four of their last five games in all competitions and the Europa League represents the only possible silverware for the Gunners this term.
However, the Premier League side have been pitted against Serie A giants AC Milan in the Europa League last 16 this month.
Former Liverpool FC defender Carragher pleaded with Wenger to accept that his time is up at Arsenal.
“In his press conference yesterday when he was talking about turning down job offers to stay here and be loyal, that doesn’t mean you should have a job for life, and they would’ve been coming 10 years ago, not now,” Carragher told Sky Sports.
“He moved Henry on, Vieira on, moved Pires on, moved Bergkamp on, legendary Arsenal players and some of the best players in their history.
“I bet some of these players could’ve joined different clubs at different times. They didn’t stay because of their loyalty though, they went because they weren’t good enough to go on.
“At this moment, what we’re seeing is not good enough for Arsenal and it has to change.”
Arsenal finished in fifth place in the Premier League table last term to miss out on a Champions League spot.
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