The Gunners, seemingly all but out of the tournament following the result at the Allianz Arena, have not reached the quarter-finals of the competition since the 2009-10 season, while the Premier League title has eluded them for the past 13 years.
With Wenger's contract up at the end of the season, former Arsenal defender Keown believes that the Frenchman may have made his mind up about his future at the Emirates Stadium.
The 50-year-old Englishman told BT Sport after the game: "He looked particularly wounded. I feel for him - he almost needs to be protected from himself.
"This is 20 years of work here. He's been magnificent for the club. This is a massive low point for him. This brings forward the change that looks likely at the end of the season.
"I think it will be him that makes the decision. The realisation that the decision needs to be made is more apparent tonight."
Wenger has been in charge at Arsenal since 1996.