United threw away a two-goal advantage in Istanbul and now face the prospect of a premature exit from European competition.
Despite United's defensive frailties bearing fruit, Ten Hag's side did produce some encouraging moments but two errors from Andre Onana allowed Chelsea loanee Hakim Ziyech to score twice from free kicks.
United remain bottom of the group hedging ino the final round of fixtures and must beat Bayern Munich at Old Trafford in two weeks to have any chance of progressing to the round-of-16.
Even then, United are pinning their hopes on FC Copenhagen and Galatasaray playing out a draw.
Following the chaotic clash, Schmeichel conducted an interview with the Manchester United boss for CBS Sports and was quick to disagree with the Dutchman's analysis of the Red Devils' collapse.
Read more on Man United
Man United on the brink of Champions League elimination after another Onana horror show
Man United star Garnacho does another Ronaldo celebration as he silences Galatasaray fans
"I'm disappointed," Ten Hag responded when asked his thoughts on United's performance. "We did many things very good but if you are twice leading 2-0 and 3-1, you have to defend better.
"And it was poor defending as a team so we should have done that better."
Schmeichel immediately hit back, questioning Ten Hag's assessment: "You say poor defending as a team? I actually have the impression the defence worked well today and defended well but it was mistakes by individuals.
"Are you worried you don't have the right kind of players to take the team to where you want to be?"
Most read in Champions League
Galatasaray goal against Man United should've been disallowed due to little-known rule
Footage captures Ferdinand's rollercoaster of emotions during Man United collapse
Real Madrid fans love what 'captain' Bellingham did for Joselu as they hail his leadership
EA FC 24 RTTK upgrade tracker, including Erling Haaland and Bukayo Saka ratings
The exchange had an awkward tone to it as the Denmark legend probed Ten Hag. However, the United boss remained calm, insisting his side must learn from their errors.
"No," Ten Hag replied. "We are in a project and so we have to learn from this and take it from here.
Rio Ferdinand has his head-in-hands after Galatasaray's equaliser against Manchester United in the Champions League
"It's all very positive how we can play and perform and to which levels we can achieve but football is a game of mistakes and details make a difference.
"We made some mistakes as a team and we got punished for it."
Later on during the broadcast, Schmeichel confirmed his question to Ten Hag was based on Onana's blunders before once again praising the performance of United's back line.
"Do you know what? I think the back four played very well today, I don't think they could have done much more," he said.
"Again though, you can't argue, the mistakes by the goalkeeper are very, very expensive.
"Every time a goalkeeper makes a mistake, it is a goal, that is just a fact of life. If you go back to Sunday, everything worked really well but when you play at this level, every little mistake you make is being penalised and you have got to learn that."