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 Wednesday night's Capital One Cup encounter with Sunderland, when United must overcome a first-leg deficit 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, although David Moyes must be tempted to include them given the avalanche of negative publicity that would accompany yet another setback.
Little has gone right for new boss 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."
Moyes is already clocking up the air miles in a bid to make the additions so obviously required.
The latest player to be linked with a move to United is Chelsea midfielder Juan Mata, who has failed to impress Jose Mourinho sufficiently to claim a regular starting berth and is beginning to fear for his World Cup place.
Former United defender Gary Neville accepts Mata does not fit the usual tactical template for United purchases.
But he knows the 25-year-old could bring an injection of positivity at a time when United appear to be enveloped in gloom.
"Does he fit in with what I would call the typical philosophy of Manchester United? I would say no," said Neville on Twitter.
"Positives of signing a player like him are obvious-lift everyone (spark) creativity, knows PL, 4th place chances go up - fantastic player."
Mata would certainly bring additional competition to an area of the field where so many feel the Red Devils are deficient.
After falling 14 points adrift of leaders Arsenal, it is now widely accepted United will not retain their title.
Yet Cleverley feels if any club can achieve the impossible, it is his.
"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."