The result puts the Gunners on the verge of exiting the European showpiece at the last-16 stage ahead of the return leg early next month, with the magnitude of the loss causing widespread anger among fans of the London side.
Arsenal are only one of three teams to qualify for the Champions League every season for the last 20 years - the other two being Bayern and Real Madrid - and Wenger was keen to remind fans calling for his head of this fact.
"Even if I go Arsenal will not win every single game in the future," he told reporters this morning. "That's part of it and you have to accept that.
"As much as it hurts to lose games, if you look at the history of Arsenal, Arsenal had [played] less Champions League games when I arrived than I'd had in my career already, and since then we've done a few.
"So I hope that in the future we can win this trophy - or Arsenal can win this trophy - but it's not like before I arrived, Arsenal had won five European Cups. They had never won it, they played maybe 10 games in the whole history of the club. So as well you have to take into perspective some demands.
"I think what is important is that the club makes the right decision for the future - I do not work here for 20 years not to care about this club. I've had many opportunities to go somewhere [else] during that period and I care about this club, I care about its future, and I think it's very important that the club is always in safe hands. Is it me or somebody else? I'm sure it will be."
Wenger has also revealed that he will announce a decision on his future in March or April.