Onana spilled Leroy Sane's 28th-minute shot into the net, conceding the opening goal at a time when Man Utd were the better team, but Ten Hag said the goalkeeper should not be blaming himself for the loss.
“[In] football on the whole, [there] will always be mistakes and this is one mistake,” the Dutchman told the club's official website. “So we also don't make it bigger than it is.
“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.”
Onana takes responsibility
Ten Hag's message came after Onana publicly blamed himself for the defeat.
“This is the life of a goalkeeper,” Onana told TNT Sports.
“It's difficult. We started very good. 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.
“We were very good on the ball. They didn't create any chances. Their first shot on target I made a mistake. It was the key point and the team went down because of that mistake.
"If we didn't win today it was because of me.
“I have to learn from it and be strong. 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.”
'It is about the team'
Ten Hag was impressed to see Onana taking responsibility but remains adamant that the loss was a collective one.
“It is good that he is doing that but it is about the team,” the manager added.
“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.”