The Cameroon goalkeeper committed two further key errors as United twice frittered away a two-goal lead to draw 3-3 in a thrilling clash in Istanbul on Wednesday night, leaving their last-16 hopes hanging by a thread.
Onana first took a fatal step to his left and was then unable to adjust properly in time for Hakim Ziyech's first free-kick which curled around the wall and into the back of the net on the goalkeeper's side.
That handed Galatasaray their first lifeline to reduce the deficit to 2-1 after early strikes from Alejandro Garnacho and Bruno Fernandes, while he later made another costly blunder to leave the score at 3-2 after Scott McTominay had initially restored United's two-goal cushion following the interval.
It was again at a Ziyech free-kick, this time Onana trying to save the Chelsea loanee's effort with one hand after an awkward bounce but succeeding only in deflecting it poorly into the back of the net.
Onana, who was later hurt after a collision with Mauro Icardi, was then beaten at his front post for the equaliser 19 minutes from time courtesy of an emphatic finish from Galatasaray substitute Kerem Akturkoglu.
It was the latest in a line of high-profile mistakes from the 27-year-old since his £47.2million summer move from Inter Milan to replace former long-term No1 David de Gea, who was allowed to depart on a free transfer after 12 seasons, with Onana tending to quickly switch between the sublime and the ridiculous on a game-to-game basis.
Such errors have contributed to United conceding 14 times already in just five Champions League matches so far this term, while across all competitions they have shipped the most goals in their first 20 games since all the way back in 1962-63.
Despite that, Onana retains the full support of manager Ten Hag, who refused to blame his 'keeper for the latest collapse in Turkey.
"He is OK. As I said, it is not about individuals," he said.
"Of course, individual errors in football can make a difference and you take responsibility for it but it is always about the team.
"This team is good, all the players in the squad are good and deserve the best to play for Manchester United because they are brilliant players.
"And that counts for the whole squad."
United's latest defensive horror show against Galatasaray keeps their last-16 hopes alive but means their fate is now out of their own hands.
Ten Hag's side must now beat Bayern Munich - who qualified as group winners with two games to spare - at Old Trafford in their final group match on December 12 and hope that FC Copenhagen and Galatasaray play out a draw in Denmark on the same night in order to sneak through to the knockouts as runners-up.
"I think as a team we played very well," Ten Hag said when initially quizzed on Onana's form. "We win and lose together. You see the progress in this team.
"I take many positives from this game. Some mistakes. We played like I want my team to play.
"It was enjoyable to watch that proactive, dynamic, brave and we scored great goals.
"Even after we had some setbacks, we kept going until the end and we should have won with big chances from Scott McTominay and (Facundo) Pellistri.
"Of course, I am disappointed because we should have managed the game better, we will learn from that. Because this team is in development."
Speaking to TNT Sports immediately after the game, Ten Hag said he was the man ultimately to blame for United not holding on for a crucial victory in Europe.
"It is always me. I am responsible for this," he said.
"We should have taken three points. This is the same in more games - home against Galatasaray and away in Copenhagen.
"We played so good. So I have to make a compliment to my team but I also have to criticise the team and us as a coaching staff and me as a manager.
"We are not defending well enough, we are leading 3-1 and you can't afford such mistakes because it makes a difference."