The Cameroon goalkeeper was at fault for Bayern Munich's opening goal as he allowed Leroy Sane's shot to squirm through his fingers.
Onana joined Manchester United from Inter Milan for £43m this summer as a replacement for David De Gea but has now shipped 14 goals in six games for his new club.
The former Ajax Amsterdam goalkeeper is the first to admit that his performances have not been up to the required standard and wants to improve as quickly as possible.
"It's difficult to lose this way because in the beginning we started very good," Onana told TNT Sports.
"After my mistake we lost control of the game. It's a difficult situation for us, for me especially because I'm the one who let the team down.
"Because of me we didn't win but we just have to move on. This is the life of the goalkeeper."
He added: "We were very good on the ball, they didn't create any chances. The first shot on target I made a mistake so I think it was the key point of the game.
"The team went down because of that mistake. I have to learn from it and be strong, move on. It's not an easy situation but I'm very happy with the comeback of the team, we were fighting until the end.
"I have a lot to prove because my start in Manchester hasn't been so good, not how I want. This was one of my worst games and it's difficult because we have big ambition. We are a big club and want to win everything.
"It's a tough time and we have to be together and continue working hard."
