The 22-year-old signed a new four-year deal with United earlier this month.
“The contract was a great bonus and I was delighted to sign,” Evans told the Manchester Evening News.
“By the end of the four years, I would like to be a regular and one of the first names on the team sheet.
“It is a big year for me next season because having just signed a new contract the expectations will go up even higher.
“I am 22 and, having signed that new long-term deal, I will no longer be classed as the young lad just coming into the squad. I will have been in the squad for two years and people will be expecting a lot of me.
“There will also be more competition with Chris Smalling coming to the club. But that is all good.
“The extra pressure won’t worry me. I put pressure on myself as much as anyone else will.
“I want to improve and become better so you have to put more pressure on yourself to perform consistently and be a more important figure in the team.”