The Red Devils had mixed fortunes last campaign as they were beaten to the domestic championship in heart-breaking fashion when neighbours Manchester City scored two late goals against QPR to clinch the title on goal difference on the last day of the season.
Their performances in Europe were very mediocre with a premature exit from UEFA's top competition but Vidic is confident they can recoil from those disappointments.
"Our aim this season is to win both the Premier League and Champions League," the Serbia international told the Daily Star Sunday.
"We had a disappointing campaign in Europe last season but I think this year will be different. We will learn from the mistakes of last year when we relaxed too much.
"Maybe we had become too complacent because we always seemed to automatically get past the group stage.
"That mentality cost us. We also had injuries - including my own - and we had a lot of younger players who were adjusting too.
"But now the younger players are a lot more experienced, and hopefully we will now have better luck with injuries."