The Red Devils capitalised on Manchester City's 0-0 draw with QPR by battling their way to a 2-1 victory over Southampton at Old Trafford thanks to a Wayne Rooney double.
But, whilst Vidic agrees that United are in a favourable position, he indicated that his side have not yet done enough to win back their crown.
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"All in all, we have to be pleased with the result," he told MUTV. "If you look at the other teams, they all drew, so we're in a good position now.
"We have to now focus for the next game against Fulham. Away games are always hard so we need to think about that.
"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."
United had to withstand intense pressure from Mauricio Pochettino's men in the second half, and the Serbian reiterated his manager's view that Saints were amongst the most impressive teams they had faced at home this season.
"We had to fight to win this game at the end," Vidic continued. "You see we couldn't have possession of the ball and they were attacking all the time.
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"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.
"Of course you have to show character. Sometimes even when it's not happening for you. You have to defend and I think the whole team was pushed to the limits physically. It was a hard game and the pitch did not help."
The 31-year-old also singled out goalscorer Rooney and goalkeeper David de Gea for praise following the victory.
"Wayne is important for the team," he added. "He is working hard. Obviously, he scored the goals and I think the more games he plays, the better he is.
"We need him, especially for the second half of the season, as we need all the players to be fit. We have a good squad now and it's going to be hard for the manager to choose the first XI.
"It was a great save from David [to keep out Rickie Lambert's free-kick]. Actually, I see the ball in the net but instead it was a magnificent save. He showed he has the talent. He is a good keeper and I think the more games he plays, the better he is going to be."