United face Barcelona again in the last game of their US tour in Washington DC later this month.
Asked about the gap between the two clubs that was highlighted by a second Champions League Final defeat in three years, Vidic said: "I have to say, I don't think so much about the gap between ourselves and Barcelona. I am thinking I have to win the Premier League and the Champions League.
"Who knows whether Barcelona will go to the final? We can speak like they are already in the final and they will win the Champions League. It's a new season. We are looking to win the Premier League. We are looking to win the Champions League. Who is going to be our opponents, we are not thinking about at this time. We are thinking about ourselves.
"We don't have any problem with the Barcelona players. We respect them but we are not scared to play against them.
"I agree Barcelona are playing great football. It is hard to take. They beat us in the final twice. It is always in your mind, but hopefully we can make it to a third one and that will be lucky for us. We have to forget what happened, take some points from that game and improve.
"From the first day I came to this club, the players and the coaches push you forward to improve.
"That is the great thing about this club. I think over the years we have improved every year. This is why we are in this position to win the title four times and play in the final three times."