The 23-year-old was replaced just before half-time by Paul Scholes as a largely second-string side slumped to a 1-0 defeat courtesy of a superb strike from Luis Alberto.
Speaking after the game Sir Alex did not sound hopeful about the midfielder's prospects of a quick return to action, with the league leaders set to make the short trip to Etihad Stadium on Sunday to face Manchester City.
|10/1||Manchester United are 10/1 to draw 2-2 with Manchester City with Paddy Power|
"He felt his calf a little but it's not good news. We'll see what he's like in the morning."
There was some good news, though, with Sir Alex revealing that Shinji Kagawa, who has been missing for the past six weeks with a knee injury, has returned to training.
"Shinji is now back and is doing some running. I don't know if he'll make Sunday's game [against Manchester City]. It might be a bit early for him," he added.
"At least he's back training and he'll hopefully join in the football part next Monday."