The 24-year-old was heavily criticized as United finished seventh in the Premier League, with fans directing their anger towards the under-performing England international.
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Cleverley was also at the center of an online petition calling for him to be dropped by Roy Hodgson on the back of his inclusion in the 30-man squad for March's international friendly against Denmark.
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"It makes you develop a lot thicker skin," said Cleverley, who was handed the captain's armband by new Manchester United manager Louis van Gaal for the preseason friendly against Roma. "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.
"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 working hard in training. 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 we've gained confidence and we’re back being a top team together."