Cleverley was heavily criticised throughout the 2013-14 campaign as United finished seventh in the Premier League, with fans directing their anger towards the underperforming England international midfielder.
The 24-year-old was also at the centre of an online petition calling for him to be dropped from the England team on the back of his inclusion in Roy Hodgson's 30-man squad for March's international friendly against Denmark.
Cleverley, who missed out on World Cup selection, is now targeting a fresh start under new manager Louis van Gaal at Old Trafford.
"It makes you develop a lot thicker skin," said Cleverley, who was handed the captain's armband by Van Gaal for United's pre-season friendly against Roma in the United States.
"You've just got to take it on the chin. It’s football. Fans are passionate and they like to see their team win. And when their team is not they have got a right to look at the team.
"And, yeah, I got a bit of stick. It does hurt when it comes to your own fans. But I’m not going to dwell on it.
"I want to prove a few people wrong. But first and foremost I am just concentrating on the next game and working hard in training and hopefully we will get back to winning ways."
Cleverley, who made 22 league appearances in 2013-14, added: "I've got to use last season as a learning curve rather than just dwell on it.
"Under the new manager we are being told to think of things as a team but personally it has gone well.
"I've got minutes under my belt, I feel fit, we've won every game - one of them on penalties - I think as a team we've got to look at it that everyone has got minutes, we've gained confidence and we’re back being a top team together."
