The former Serbia international is convinced the Red Devils will put their disappointing European performance last season behind them as their young players grow more experienced
On Sunday, Goal.com exclusively revealed the three-time European champions could cash in on the currently injured centre-back, with Russian side Anzhi Makhachkala interested in the 30-year-old's services.
Despite narrowly missing out on domestic glory in the final minutes of last season to rivals Manchester City, Sir Alex Ferguson's men suffered an early exit from the Champions League after failing to get past the group stages.
But Vidic says they have learnt from past mistakes and is still confident success can be achieved on all fronts this season.
"Our aim this season is to win both the Premier League and Champions League," the retired 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."