United conceded three goals against Phil Brown's side in the 4-3 win at Old Trafford on Saturday and Vidic is looking for an improved defensive display when they visit Celtic Park to face Gordon Strachan's side on Wednesday night.
"The most important thing is that we took the three points," Vidic has said.
"We made a few mistakes and lost a few goals, which is not good for us, especially the defenders.
"We can learn from the game. We made small mistakes that cost us three goals.
"I hope we can improve on that so it doesn't happen again.
"We need to forget this game but not how we conceded the goals.
"That way we can make sure it doesn't happen again. We have a few days to work on that before Celtic and to improve.
"The first goal was from a set-piece and the third came after we had a corner and we were out of position, so they were able to counter-attack.
These are small mistakes that don't usually happen with us.
"We need to learn from our mistakes but we don't need to be too worried."