The Cameroon international arrived during the summer transfer window as a replacement for long-serving goalkeeper David De Gea, having worked with manager Erik ten Hag at Ajax.
Heralded for his ability to play out from the back during his time with Inter Milan, Onana has struggled during a rocky start to the season for United.
They are on their worst defensive run since December 1978 and are threatening to undo the work ten Hag did to bring the team along during his first season in charge.
After a positive start for United inside the Allianz Arena on Wednesday night, the 27-year-old allowed Leroy Sane’s snapshot underneath him to hand Bayern the lead.
Serge Gnabry doubled their advantage fewer than five minutes later before Rasmus Hojlund gave the away side hope.
Harry Kane would then add a penalty after Chrisitan Eriksen was adjudged to have handled inside the box before there was late drama.
Casemiro turned in a United second, only to see Mathys Tel fire in a fourth for the German champions but the Brazilian would then score a late third in the dying embers, though there was no more time to mount a comeback.
"It’s difficult,” Onana told TNT Sports.
“We started very good. After my mistake we lost control of the game. It’s a difficult situation for us, for me.
"The team were one down because of that mistake. I have to learn from it and be strong. I’m happy with the comeback of the team.
"I have a lot to prove. My start in Manchester hasn’t been so good, not how I want. This was one of my worst games. We have big ambition.
"It’s a tough time. We have to be together and work hard."