However, the 68-year-old insists he is only anxious about Thursday's Premier League clash with Pep Guardiola's side, having spent much of his two decades at Arsenal dismissing speculation about his job.
Thursday's game, rather disconcertingly for Wenger, sees leaders City visit the Emirates Stadium for a league clash.
Wenger has come under mounting pressure at Arsenal because of a failure to challenge for the Premier League title in recent years.
Arsene Wenger's position will be reviewed at the end of the season. I am just amazed that I have to always answer things that are exactly the same.
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"My position is my position".
On the Wembley defeat, Wenger said: "I'm quite amazed at how people analyse (the cup final) it looks like we lost against a team in division five - we lost against a team that dominates English football at the moment". Eliminated from the FA Cup in humiliating fashion by second-tier Nottingham Forest in January, Arsenal is languishing in sixth place in the Premier League, 10 points adrift of the top four with 11 games left.
Wright says the time has come for a change of manager, with Wenger having been at the helm since 1996.
Arsenal face AC Milan in the last 16 of the Europa League next month, a hard assignment in a competition that still includes Atletico Madrid and RB Leipzig as unsafe potential future opponents. It will take them a few years.
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And although Ian Wright was also critical of Wenger, the Arsenal legend also claimed that he had been badly let down by his players.
"Yes, of course [they gave me everything]", Wenger said. "But we have as well to win big games because if you want to go far in the Europa League you have to win big games". We played against Chelsea and we have shown that we can fight.
Former Arsenal striker Thierry Henry, part of Belgium's coaching team, suggested while working for Sky Sports on Sunday that managing the club could happen in the future. "That being said i can't accept some of the decisions that went against us yesterday". We have to play Basel first.
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