United are reeling from Sunday's 3-1 defeat at Chelsea, which left them six points adrift of a Champions League berth and without skipper Nemanja Vidic for three games following his red card for a lunge on Eden Hazard.
It means the Serbian will be suspended for the visit of the Black Cats to Old Trafford, when United must overcome a 2-1 deficit from the first leg to reach the final and a probable showdown with in-form rivals Manchester City.
Neither Wayne Rooney nor Robin van Persie are likely to start given they have only just returned to training following groin and thigh absences respectively.
Little has gone right for new boss David Moyes this season, but Cleverley is adamant United will not let their heads drop.
"We can't let it get our heads down," he told Sky Sports News. "You have to feel for the new manager. He has had no luck at all. But we are not going to feel sorry for ourselves.
"We have to stand up and be counted. That starts with the Capital One Cup."
Cleverley has still not written off United's faint chances of retaining their Premier League title despite currently trailing leaders Arsenal by 14 points in the title race after their seventh league defeat of an inconsistent campaign.
"You can never rule Manchester United out," he said.
"This club has come from some mad positions in the past to go on and win things.
"It is going to be very tough. I would say we will need to win every game from now until the end of the season to do it but you should never rule us out."
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