Young, who only appeared as an 84th minute substitute during the game, injured his shoulder after landing awkwardly following a controversial collision with Tottenham goalkeeper Hugo Lloris.
Immediately after the game, David Moyes branded Howard Webb's decision not to award his side a penalty and send Lloris off following the challenge as 'scandalous.'
"Ashley has got an injury that is going to keep him out for a time," said Moyes.
"It is a shoulder injury he received in the challenge by the goalkeeper. I am not sure how long it will be."
The unpunished challenge on Young has reignited the debate over widening the use of video technology but Moyes insisted he did not feel the incident merited a rethink on the use of video replays.
"I wouldn't go down the route of video technology," said Moyes. "I trust the referees to make the right decisions.
"They do make the wrong ones at times and I have not changed how I felt on Wednesday. I thought that was the wrong decision."
Young's enforced absence is the latest concern for United who have suffered with injuries to key players including Nemanja Vidic, Patrice Evra, Michael Carrick and Rio Ferdinand and various stages during the season.
Wayne Rooney is reportedly managing a groin problem while Robin Van Persie has missed the club's last six matches with groin and thigh injuries.
Moyes offered no update on Van Persie's return to action but insisted the club's recent injury woes will have no bearing on any potential transfer business in January
"We will let you know when he is ready," said Moyes. "It won't change how we go about things,"
"January is not an easy month to purchase in.
"We have a good, big squad that is getting stretched at the moment because of the number of games.
"But everybody picks up injuries at this time of year. We are no different and we will use the players."