Bayern repeated their 5-1 first-leg win in Tuesday's second leg to condemn Arsene Wenger's side to their heaviest defeat at the Emirates Stadium since they moved from Highbury in 2006.
It is the seventh year in succession that Arsenal have gone out of the Champions League in the last 16. "It's a sad day because we've gone out again at this stage. We're going through a period in our history that's the worst," Wright, who played under Wenger, said on BT Sport.
"With everything that's going on, you have to say it will take some sort of monumental effort for Arsenal to turn it around in terms of the drive and determination of the players. It feels like something is coming to an end."
Wenger, who has been Arsenal manager since 1996, is out of contract at the end of the season and was the target of a protest from around 200 disgruntled fans prior to Tuesday's game.
At the final whistle, some fans held up banners calling for him to leave. Wenger has said he will make an announcement about his future either this month or next.
"He looks like a lost man," said Wright. "It just seems to be mounting up. You've got the fans, the protests. It's imploding."
Wednesday's British newspaper sports pages put the boot in, with several screaming "WENGER OUT" in a nod both to Arsenal's elimination and the calls from supporters for him to step down.
The Daily Express headlined its match report "SHAME AGAIN" and The Times said Wenger had hit an "all-time low".
The Daily Telegraph said Arsenal had been "humiliated", with Wenger "urged to quit by fans", while The Guardian said he had been left "staring into the abyss".
The Daily Mirror focused on a picture of Arsenal forward Alexis Sanchez supposedly smirking on the bench after being taken off, beneath the headline: "LAUGHING STOCK".
Wenger, 67, revolutionised Arsenal after arriving in England as a virtual unknown from Japanese club Nagoya Grampus Eight in September 1996.
He led the club to three Premier League titles and four FA Cups in his first nine seasons, including the famous 'Invincibles' league campaign of 2003-04 when Arsenal went 38 games without defeat.
But the years since have yielded only two FA Cup successes, in 2014 and 2015, and while Arsenal have continually qualified for the Champions League, they last reached the semi-finals in 2009.
A recent run of three defeats in five games has seen Arsenal drop out of the Champions League places in the Premier League.
Their best hope of silverware lies in the FA Cup, with non-league Lincoln City due to visit the Emirates in the quarter-finals on Saturday.