Varane was knocked down at the edge of United’s penalty area and had to go receive treatment to ensure he was okay.
However, the Frenchman didn’t go down the tunnel for treatment upon his withdrawal.
Giving an update, Ten Hag detailed that the injury was significant enough to bring his afternoon to an early conclusion.
“I don’t think so, that he would have carried on [if the score would have been closer],” Erik responded to a question about the defender’s substitution, in his post-match press conference.
“But you get him off because when you are 4-0 down, you don’t want to take a risk to get a bigger injury.
“But I think it’s that big, the injury, that he couldn’t carry on.”
The boss will likely provide a further update on the defender in midweek, ahead of the Reds’ upcoming Europa League game away to Omonia Nicosia on Thursday.
United have already lost one centre-back to injury in the last week, with Harry Maguire ruled out following the recent international break.
Victor Lindelof replaced Varane and played the remainder of the game at the Etihad Stadium alongside Lisandro Martinez in the middle of Ten Hag’s defence.
Speaking about his team’s status, Ten Hag stated that despite the loss to City, they were still in good shape as shown in their performance against Liverpool and Arsenal.
“I think it’s good that a team like City gives you the status where you are in this moment. It’s clear we did well against top teams like Liverpool and Arsenal, when we were disciplined and we followed the rules and principles, we had belief to play and we were on the front foot defending. Then you can bring a good performance and that can bring a result. When you don’t, when you are not front foot, when you are not brave to play, you get the result as today.”