The latter has endured an injury-hit season and may have returned at the just the right time given Rashford pulled up shortly after providing the assist for the Frenchman’s goal.
The 27-year-old sharpshooter held his groin after trying to meet a Christian Eriksen ball over the top and immediately indicated to the bench that he was hurt.
The dejected forward trudged around the pitch with a heavy limp and was consoled by Ten Hag before heading down the tunnel, with the manager later saying he “doesn’t look well”.
“I can’t say in this moment,” the United boss said. “You are a doctor, maybe I’m not.
“We have to wait – how bad or how good it is. So, yeah, obviously he went off with a complaint and now we have to wait, set a diagnosis and then we can see.
“Also, when I asked now the doctor I get the same answer.”
This was United’s third Premier League match in seven days, having lost 2-0 at Newcastle last Sunday before beating Brentford 1-0 on Wednesday evening.
Asked what his solution to the fixture calendar was after Ten Hag told BT his injury was “due to the schedule”, the Dutchman said: “Some things you can’t avoid but that was avoidable.
“Why is the Premier League giving us the late Sunday night game and giving us the early Saturday game? I think it’s not right.
“Then you run the risk. The players can’t recover that quickly and we know all the science, all the science research that will give you that players need a certain period to recover.
“If it’s more (games) after each other, then it accumulates so then they run even more the risk.
“It’s also part of the schedule that we are now finding ourselves in this situation and now we can only pray that (Rashford) is not dropping off.”
An injury lay-off for Rashford would be a huge blow for United, who are pushing to add the FA Cup and Europa League to their Carabao Cup triumph as well as pushing to finish in the top four.
“This was avoidable, it was not necessary to set the schedule like we have now,” Ten Hag said, after a match when his side scored only two of their 29 attempts.
“Then I think other facts is more important than the sportive element, like protecting the players.
“Also, let’s say this, today we have seen a very entertaining afternoon, but players can’t do it so often when they are not fresh.
“We create a lot of chances but missing the chances is also part of it, that is a lack of freshness in the final moment, and the risk of injuries.
“I think we have to protect the players and that is also the interest from the total football because everyone wants to see great football. Then you need to have your best players on the pitch.”
Everton were fortunate not to be on the end of a first-half hiding and manager Sean Dyche knows his side rode their luck at Old Trafford.
“They are a very good side, for starters,” the Toffees boss said. “They’ve proved that with their home record.
“Too many mistakes from us, to be honest. They were the dominant force in the first half. Lots of long balls, which we didn’t deal with very well by our standards.
“So, pretty simplistic, really, in what we could have done better.
“But there was still some really good last-ditch defending when we had made mistakes, so it wasn’t like we’re just making the mistakes and not trying to make up for them.
“But the reality was not doing the basics well enough in the first half as a collective and they should have been further in front.
“Although, ironically, we had probably the chance of the game, with young Ellis Simms, which may have changed the feel of what was going on at that stage because it was 0-0.”