The 25-year-old England international pulled up with an apparent groin injury towards the end of the match.
When it was mentioned to Ten Hag that the damage looked serious, the Dutchman replied: “You are a doctor?”
However, he had already told us of his concerns and then complained about United’s schedule, which involved them playing a late Sunday game last week and an early Saturday one in this round of fixtures.
“We have to wait. He doesn’t look well,” Ten Hag said of Rashford.
“This was avoidable. All science and research tell you players need a certain time to recover.
“It is also part of the schedule that we are now finding ourselves in this situation and now we can only pray he is not dropping off.”
Ten Hag conceded he could have taken Rashford off once United had their second goal 19 minutes from time, but opted against that move because he wanted his leading scorer to get game-time alongside the returning Anthony Martial.
“I don’t think any manager at this stage of the season will rotate so much,” he said.
“I had the consideration [to take him off] but in that moment, with Anthony Martial just coming back, you want to bring them back into routines and togetherness.
“When they are together we have two goalscorers who can finish games, which is what we need in the final stage of the season to be successful.
“Also, there was no indication. If there was an indication I would have taken him off.”
Ten Hag was happier about the performance of skipper Harry Maguire, which he says he has not seen previously.
Maguire has featured for just five minutes across three home Premier League games since he started against Bournemouth on 3 January.
The £80m man told BBC Sport after the 2-0 win against Everton he “has a responsibility to make sure the club moves forward whether I am playing or not”.
Evidently, he would prefer to be on the pitch and Ten Hag said Maguire’s contribution to a win that consolidates United’s top-four position was exactly what he is looking for.
“That was a different Harry Maguire to what I’ve seen in the first weeks and months,” said Ten Hag.
“It’s not been that easy for Harry but the demand is on him. He did really well today, in and out of possession, dominating his opponent, dictating and bringing passes.”
Whether that is enough for Maguire to retain his place for Thursday’s Europa League quarter-final with Sevilla remains to be seen, given Raphael Varane was an unused substitute.