The Cottagers travel to Old Trafford at the weekend in the fourth round of the competition and Cleverley intends to be all over the opposition.
"At home, if we've got teams under a lot of pressure, they can struggle if we don't give them a second to breathe," said the 23-year-old England international, quoted in The Sun.
"We've played some really good stuff - fast, one-touch football."
Asked how important the competition is to United, Cleverley said: "It means a lot. Our last FA Cup win was in 2004 and it's a trophy I want.
"Playing at Wembley is one of the best feelings of your career. I've been lucky enough to have played there five or six times but I always want more.
"We've got a few players who haven't won anything in this country yet - like me. So anything we're involved in, I want to win.
"At the start of the season, the first thing I wanted was to be injury-free. I want to make as many appearances as I can and help the team win some silverware.
"We've got the experience of last year and we know how hurt we were. There's a great team spirit now. There was last year, too, but there's a good feeling around the place, which is fantastic.
"To me, it just feels like a group of winners."