United's goalless draw at Arsenal was creditable given that the Gunners have lost just once at home this term, but the fact remains that David Moyes' team are now even bigger outsiders in the race for Champions League football.
The last time United failed to qualify for European football's blue riband competition was in 1995 when Cleverley was just six years old.
To make sure the team make the grade this term, the United midfielder thinks the Red Devils must win all their remaining games, including their meetings with Liverpool, Manchester City and Everton.
"We need to win every game from now on," said Cleverley, who was dismayed to hear about Steven Gerrard's match-winning strike at Craven Cottage when he came off the pitch at the Emirates.
"Liverpool getting a last-minute winner is disappointing for us
Our result isn't the worst in the world but we need to start winning games fast.
"We showed we are resilient, that we are still fighting for every point but unfortunately we have lost more ground on the teams around us so we have to really get our heads down and start winning quickly at Crystal Palace in 10 days."
Although Moyes is yet to admit it publicly, United have next to no chance of retaining their Barclays Premier League title.
The bookmakers rate United as 450-1 shots, and they rarely get things wrong.
The obvious secondary target for the reigning champions is now a top-four finish - something the bookmakers also do not think United have much chance of achieving.
Moyes' team sit 11 points off fourth-placed Liverpool with 12 matches left, but the United boss hopes a warm-weather training camp will help his players, who looked leggy towards the end of the Arsenal game, recharge their batteries.
Cleverley recalls that United only lost two of their final 15 matches following a January camp in Qatar last year and the 24-year-old is hoping for a similar impact from the trip to Dubai.
"We will get some warm weather training, we will be getting the lads together, and it will help team spirit," the England midfielder said.
"We did it last year and it had a good effect on us so hopefully it will have the same effect this year."
Cleverley and the other midfielders in Moyes' squad have been the reason behind United's rapid decline this season, according to many.
Moyes himself admitted earlier this month that he wanted to add a central midfielder to his squad in January even though he signed Marouane Fellaini for ?27.5million in the previous transfer window.
Cleverley and Michael Carrick performed well at the Emirates, though, stifling the creativity of the likes of Mesut Ozil, Jack Wilshere and Santi Cazorla.
Carrick has not been fazed by the criticism that he and his midfield partners receive.
"We get stick all the time
We are used to it," the former Tottenham midfielder said.
"I thought we did a good job against Arsenal, not just in midfield as a unit but as a team.
"Robin (van Persie) and Wayne (Rooney) took up good positions
At the same time we had to defend as well.
"We limited them to not much space around the box and not many chances
You could see their fans were getting frustrated
That is when I thought we might have nicked one and made it a fantastic night."
Source : PA