The Brazil international received lengthy treatment following a clash of heads with Fulham's Harrison Reed early in the second period, and he then headed down the tunnel after it became clear that he would be unable to continue.
Ten Hag has admitted that he is unsure whether Casemiro suffered a concussion, but the midfielder will now need to be assessed ahead of Wednesday's FA Cup fifth-round contest with Nottingham Forest.
"I don't know if it's concussion but it's definitely head to head. I actually don't know [the issue] but he had to come off. He had to come off so we have to speak with the doctor, and the medical team, to see how he's doing," Ten Hag told reporters after the match.
"He couldn't continue the game. We have all seen that. We had to take him off and, hopefully, he's better by tomorrow."
Man United were beaten 2-1 by Fulham on Saturday afternoon, with Alex Iwobi scoring a last-gasp winner for Marco Silva's side at Old Trafford.
"We had strong belief. We went for the win. That is, I think, the character from this team so I think that's great to see but don't let them escape. They come out from a throw-in near the corner and it shouldn't happen," Ten Hag told reporters after the match.
"We have them under pressure but one player is in the wrong position. So, as a team, we should manage that so everyone is in the right position. We have experience on the pitch.
"We let them escape and that was avoidable. It can't happen when an opponent has a throw-in. The team has to make sure the positions are good and look for detail.
"We get punished. I think that was more that mistake [than anything else] and, before that, we went for the win. I think we should have rewarded ourselves by taking the opportunities."
Rasmus Hojlund was missing for Man United due to a muscular problem, while Luke Shaw was another notable absentee for the hosts at Old Trafford.
"It's not only Rasmus. It's Luke Shaw. Casemiro fell out, shortly after the break, so it's a lot of change in the team. Of course, that has consequences," added the manager.
"You don't play the same levels as we did last week. When they are not available, we have to deal with it. We could have won this game, also with this squad today, we should have won this game. We scored today as well, and we know we can sort it out, but, of course, we prefer he is available."
Man United sit sixth in the Premier League table, three points behind fifth-placed Tottenham Hotspur and eight from fourth-placed Aston Villa in the battle to secure Champions League football for next season.