The 24-year-old secured his first title medal in last term's campaign when United snatched the trophy back from rivals Manchester City.
"It's a relief to get the first medal, but it also makes you determined to win more," Cleverley told Inside United. "Experiencing that victory parade is something you want to do again and again and again.
"It was a very special day, which I'll never forget, but I don't just want that to happen once, I want it to happen many times. We've got that taste now and it makes us even hungrier."