The young midfielder made his league return at Goodison after a foot injury but fans will have feared the worst after he hobbled off on 55 minutes.
However, Sir Alex has declared that Cleverley's problem is not too serious and he was taken off as a precaution.
"He's felt his ankle again," the manager told MUTV. "It's nothing serious, just tightness and tiredness. It's his first real game back, although he played on Tuesday [at Aldershot] of course. He should be okay next week and it was an excellent performance from him in the first half."
The news is less good for defender Chris Smalling, though, as the former Fulham man has a fractured toe and faces a month on the sidelines and Ashley Young, who could be missing for a fortnight.
"Smalling has a small fracture on his foot," added Sir Alex. "I think he'll be out for a month and it's unfortunate that one.
"Ashley Young has a toe injury that is not going away so he could be out for a couple of weeks."