The Red Devils lost 1-0 at Everton in their opening game of the 2012-13 campaign on Monday, and the 23-year-old has urged his teammates to bounce back at Old Trafford.
"After the result on Monday, Saturday's game is a big one for us and we need to bounce back," he told United's official website.
"Everton away is always going to be a hard game and they played very well to be fair.
"We've really got to get our season up and running on Saturday and pick up three points."
Cleverley was part of Team GB's London Olympics squad and made his debut for England in their 2-1 victory over Italy in a friendly international earlier this month.
The 23-year-old then started against Everton on Monday for United and is pleased with his personal progress of late.
"Monday was very disappointing but on a personal level it was really nice to start the season again," said Cleverley.
"Winning my first England cap the week before was a big landmark for me and a great way for me to begin things.
"I feel 100% fit and really sharp and I just can't wait to get back out at Old Trafford."
Cleverley is likely to start against Fulham at Old Trafford alongside Paul Scholes, Shinji Kagawa and Ryan Giggs in midfield.