The midfielder was one of a number of players who enjoyed their first championship triumph last term and Cleverley hopes the celebrations that followed are something he will be able to experience many more times in the future.
"It [the day of the victory parade] was a very special day and something I'll never forget," he told ManUtd.com.
"I don't just want to experience that once - I want it to happen many times. We've got that taste now and it makes us hungry.
"It maybe takes a little bit of pressure off [winning your first one], but being part of that victory parade makes you want to do it again and again throughout your career."