The 27-year-old headed the opener in the fourth minute as United defeated the Italian champions 2-0, with Cristiano Ronaldo adding a second just after the break to send the club into the UEFA Champions League quarter-finals.
But the holders did not have things all their own way with Inter threatening on a number of occasions.
Swedish striker Zlatan Ibrahimovic saw his header come back off the bar before second-half substitute Adriano hit the inside of the post with a left-footed volley.
"We need to forget Inter now," said Vidic.
"Liverpool is the next big game we must play and they are in good form, full of confidence. They had a great win against Madrid.
"But we're at home in front of our crowd and, I think, I hope we are going to be much better than we were against Inter.
"We will definitely try to improve, to erase the mistakes we made and play better against Liverpool."
With Liverpool seven points behind their bitter rivals, having played a game more, a defeat on Saturday would surely spell the end of their title challenge for another season but Vidic is not thinking that far ahead.
"I don't like to say. If we win we will be 10 points in front of them, but I don't like to think that far," he added.
The former Spartak Moscow man's header on Wednesday was his seventh goal of the season, more than any other campaign, but he admits he can not pinpoint a specific reason for his improved form in front of goal.
Goalscorer"I've definitely not scored more than I have this season, so I'm happy," he smiled.
"But I can't really explain why I've scored so many. It's something that's just happened.
"I can say we have had great crosses this year, and then I try to take up a position to score a goal. Maybe I'm just more lucky than in previous years."
However, Vidic does insists his opener against Inter was one of the most important goals he has scored but declared the fact that the team kept another clean sheet, their sixth in this year's competition, gave him more pleasure.
"It was an important goal for the team, for myself," he highlighted.
"First of all it is my job as a defender to stop people scoring and we are happy we didn't concede a goal.
"Inter did have two very good chances but at the end of the day we won and now we need to focus on the next game."