The club captain broke down during Sunday night's defeat at Aston Villa.
Dalot remarked afterwards: "It's massive. We don't know how bad it is but for him to come off, we know how tough he is. Hopefully it's not too bad and we keep with him for the next games.
"This is the time that opportunities come for other players and the time you step up and show you deserve to be in the team and play more minutes.
"I think that's how the players who get opportunities should look at it. We are Manchester United and we have to find a way to win."
On the defeat, Dalot also said: "We had good moments in the game. We kept pressing them high and knew they wanted to play long and if we won the second ball we could control the game. I think we did it quite well in the first half with one or two chances.
"They had a great first goal and credit to Morgan Rogers, it was a great goal. The second half we tried to do the same things. On the ball we were comfortable and could have tried to find the spaces in behind because they had a quite high line.
"We did enough to score more goals. We couldn't take the chances we had and that's overall for today."