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Erling Haaland and Phil Foden both scored hat-tricks as City produced a dominant performance against their rivals on Sunday, though a second-half brace from Anthony Martial and a long-range strike from Antony allowed the Red Devils to salvage some pride.
As a result, Ten Hag joined United predecessors David Moyes, Louis van Gaal, Jose Mourinho, Ole Gunnar Solskjaer and Ralf Rangnick in losing his first Premier League match against City.
Asked what went wrong for United, who came into the game on the back of four successive league wins, Ten Hag said: "A lack of belief.
"I'm surprised, why we didn't bring it on the pitch. I've seen – since, obviously, four weeks ago – a different team, a different spirit, a different fight and a level of commitment.
"Today we didn't have commitment. From the first minute on, we were not on the front foot, we were not brave in possession"
Pushed on why he thought United fell short of their recent standards, the Dutchman added: "It's always difficult to find out.
"I have to talk with my players and find out. They know they got better [in recent games], I saw the performances against Arsenal and Liverpool.
"But if you don't fight, which they didn't, then you have a problem against a team like Man City."
Monday's (AEDT) defeat represents just the fourth time United has conceded six goals in a Premier League match – two of which have come against City (also in a 6-1 loss in October 2011).
United's last league reverse was also a comprehensive one, but Ten Hag said the defeat at the Etihad was not comparable to last month's 4-0 thrashing at Brentford.
"I don't think you can compare it," he said. "It's definitely like it was against Brentford mentally, but it's different.
"Against Brentford we didn't run. Today, we wanted to run, but we didn't follow the principles or rules. Once again, it was a lack of belief."
While Ten Hag was pleased with Martial's contribution following his second-half introduction, he said it was impossible to take many positives from an "unacceptable" display.
"He had a really good pre-season and I'm happy for him that he scored goals, and also for Antony, but in this moment I cannot express for the outside world always positives," Ten Hag said.
"We are highly disappointed about this result and that has to be the tone for this Sunday. We have to accept that, but our performance is unacceptable.
"As a team, as individuals, we will criticise each other tomorrow, and then we have to learn the lessons and do better, starting next game.
"A team like City, they give you the status where you are at this moment. We did well against top teams like Liverpool and Arsenal. We were disciplined and followed the rules and the principles and we had the belief to play.
"We were on the front foot in defending and you can bring a good performance and a result.
"When you're not on the front foot and when you're not brave enough to play, you get the result like today."