The Cameroonian allowed a tame strike from Leroy Sane to squirm through his arms in the European contest at Allianz Arena, with the mistake giving Bayern the lead against the run of play.
The German champions went on to record a 4-3 victory in the Group A opener, with Serge Gnabry, Harry Kane and Mathys Tel also on the scoresheet for the hosts, while Rasmus Hojlund and Casemiro (two) registered for the 20-time English champions.
Onana said after the match that he was to blame for Man United's loss, but Ten Hag has insisted that a number of factors contributed to the defeat in Munich.
"[In] football on the whole, [there] will always be mistakes and this is one mistake. So we also don't make it bigger than it is," Ten Hag told reporters during his post-match press conference.
«This was not just Andre and then, after that, he made, in the second half, great saves for us and he shows his capabilities and abilities. He will bounce back, and he is a very important player.
''It is good that he is doing that (owning up to his mistakes after the match) but it is about the team. Always mistakes are being made, but you have to bounce back as a team.
»When you score three goals as Manchester United once again, and one player makes such a mistake, it is done, it is gone.
«That is what we, as a team, we have to believe that we always can bounce back. Tonight we showed it, that if you stay in the game and you fight for yourselves in the game, and must keep going, even after the mistakes.»
Ten Hag also opened up on his side's disappointing run, which has seen them lose three games inRead on sportsmole.co.uk