The Red Devils were dramatically pipped to domestic glory on goal difference by Manchester City in May, however their challenge in Europe's top competition ended surprisingly early.
Following failure to beat Benfica or Basle in two attempts, Sir Alex Ferguson's men slumped to a disappointing third-place finish in Group C.
Vidic has blamed his side's downfall on complacency, but he is confident of making a marked improvement this term.
"Our aim this season is to win both the Premier League and Champions League," he told the Daily Star. "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."
United have made a perfect start in Group H this season, recording narrow wins over Galatasaray and CFR Cluj.