United went though a mid-season injury crisis during the last campaign, with the likes of Rio Ferdinand and Nemanja Vidic out sidelined for lengthy periods.
The problems meant there was an opportunity for Evans to force himself into the reckoning, however the Northern Ireland international experienced fitness problems of his own.
And the 22-year-old told The Sun that he felt like his chance to become a first team regular had passed.
He said: "It was so frustrating because I picked up a few niggly injuries.
"It was annoying that with players like Rio Ferdinand and Nemanja Vidic out injured as well, there were chances to get in and get a few games under your belt."
Evans recently signed a new four-year deal at Old Trafford, meaning he still has plenty of time to develop into a household name at the Premier League giants.
The defender now hopes to put his injury problems behind him and become Sir Alex Ferguson's first-choice centre-back.
He added: "There were windows of opportunities I couldn't take because I was sidelined.
"By the end of it (the contract), I'd like to be the one of the first names on the team sheet."