With the Citizens held to a goalless draw by basement club Queens Park Rangers at Loftus Road on Tuesday night, the Reds Devils are now clear favourites to win the title.
But Vidić urged his team-mates to take one game at a time as the 19-time English champions look to wrestle the league crown from their derby rivals.
“It’s a good position we’re in,” he told United’s website. “It’s important to win games, especially at this stage of the season, and every game now is important.
“We know that we have to forget the games that come before and always focus on the next ones.
“Nothing is finished yet. There is a long way to go but we’re in a good position.”
Vidić also praised United’s battling spirit after securing three points against the Saints despite an unconvincing display.
“We had to fight to win this game at the end,” he added. “You see we couldn’t have possession of the ball and they were attacking all the time.
“Sometimes it’s important to win this type of game. Obviously, the performance in the second half, we’re not really pleased with, but I think we played some good football in the first half and had some good chances.
“All in all, we have to be pleased with the result. If you look at the other teams, they all drew, so we’re in a good position now.”
ENHANCED ODDS: Get 10/1 on Arsenal to beat Chelsea