Updated 11 September, 15:45
It was feared the midfielder, who has started the campaign in fine form, had broken a bone in his foot after feeling the full force of a Kevin Davies tackle just before Javier Hernandez's opener at the Reebok.
But the boss told ManUtd.com on Sunday that Cleverley has suffered ligament damage to his foot rather than a fracture.
The manager also said the club's medical team would assess second half knocks to Patrice Evra and Jonny Evans, ahead of the Reds' Champions League opening group game against Benfica in Lisbon.
"We'll see them on Sunday," he told MUTV. "Jonny is doubtful for Wednesday - he got a knee in the hip in the second half which was pretty painful, while Patrice got a kick on the kneecap. We'll have a look at them on Sunday - it's too early to say [how serious the injuries are]."
Sir Alex confirms Tom Cleverley will be out for four weeks after suffering ligament damage to his foot. Thankfully, there is no fracture.
Boss on Evans and Evra: "Jonny got a knee in the hip in the second half which was pretty painful and is a doubt for Wednesday [against Benfica], while Patrice got a kick on the kneecap. We'll have a look at them on Sunday."