Memories of last season's title celebrations that followed still linger for the England midfielder.
And like so many of his team-mates have found down the years, now Cleverley has experienced the winning feeling, he does not want to lose it.
"We've got the best examples ever," said Cleverley.
"The desire from (Ryan) Giggs, Rio (Ferdinand), (Paul) Scholes, Wayne (Rooney) is what you want.
"They have all won a number of titles and they're still so hungry to win more.
"We follow on from that - that feeling passes down to us.
"We want to be here in 10 years saying we've got six, seven or eight medals. You're brought up like that at this club."
The most satisfying part of last season for Cleverley was the manner in which United responded to the loss of their title to Manchester City.
Not for them the nail-biting last-day drama of an injury-time championship triumph.
The Red Devils achieved their aim with four games to spare and eventually settled for an 11-point advantage over City, who could not use bad luck as an excuse.
"We did really well last year," said Cleverley.
"We didn't just win it, we won it in style after the previous year, which really hurt us.
"We want to retain the title now. The victory parade was incredible and makes us want to win more and more, especially those of us for who it was the first time.
"We want to be there again and again, going through Manchester on that bus."
Yet Cleverley has a personal battle ahead of him.
One of the key components in Roy Hodgson's England World Cup squad, Cleverley is heading into the unknown at Old Trafford.
For with Paul Scholes retired and Darren Fletcher facing major question marks over his future, new manager David Moyes has made strengthening his midfield a priority.
A move for Barcelona's Cesc Fabregas is already under way, whilst Everton's Marouane Fellaini and Yohan Cabaye from Newcastle have been linked with Old Trafford moves.
It does not faze Cleverley though.
Speaking after Saturday's 5-1 win over an A League All Stars outfit at ANZ Stadium, the 23-year-old insisted no amount of speculation will disturb his focus.
"There will always be world-class competition at a big club like this," he said.
"Manchester United gets linked with big players. It's no different this year but I don't really take much notice of it.
"I just play my football."
Cleverley admits he has enough on his plate getting used to a new manager.
"We always had to impress Sir Alex Ferguson. He challenged us every day.
"Now David Moyes is in charge but the aim is no different. We are all working hard to impress him."
Although United's original intention had been to fly straight out of Sydney last night on the near 10-hour journey to Tokyo, once it was established airport restrictions would stop them, it was decided to stay on for another full day.
It provides a further opportunity to take advantage of the state-of-the-art facilities that have been on offer before an overnight flight takes them to Japan for two games in three days and a reunion with Shinji Kagawa.
Back home in England, chief executive Ed Woodward will continue to hunt for new players ahead of that opening Premier League encounter at Swansea on August 17.
There were definite signs Moyes' squad are stepping up their own preparations last night with a much-improved performance, during which Danny Welbeck and Jesse Lingard both scored twice and Wilfried Zaha also impressed.
"All the lads would say the Thursday and Friday sessions were really sharp," said Cleverley.
"We've definitely hit that extra gear. You can definitely see in training that the intensity has stepped up and the players are getting to know each other better.
"All the boys are really enjoying the new manager's training.
"We are moving forward and we want to keep it like that."