The Premier League champion is four points behind its rival with Sir Alex Ferguson's side having a game in hand, but the assistant manager says it has to pounce on slip-ups.
Following a 2-0 win over Fulham, last year's champion trails Sir Alex Ferguson's side by four points having played 23 games; United plays at Tottenham on Sunday, and Platt believes that his side must only focus on its own results.
"[Winning games] is all we can do," Platt told reporters. "We've got 15 left, United have 16 left.
"Both teams will drop points between now and the end of the season but we've got to make sure that we keep getting victories and if United do slip up we’re in a position to take advantage of that.
"But we can’t do anything about what Manchester United do, we can only look after ourselves, so our focus and concentration is on making sure we win as many games as we possibly can and get the points.
"I think we’re three goals worse off than Manchester United. I think if we make the seven points up then the goal difference will get made up but we can’t dictate what Manchester United do."
The game marked Sergio Aguero's return to action following an injury layoff, and Platt says the staff is pleased to have the Argentine back playing. The former England international also revealed that Pablo Zabaleta, who picked up an ankle knock during the match, should not be out of action for too long.
He added: "It's two weeks since [Aguero] did the injury. He's trained since the beginning of the week and stepped things up – he’s been with the team full-time for the last three days.
"It wasn't a case of throwing him in when you shouldn’t throw him in to win a football match but for him to go in there, play 15 minutes and get that under his belt.
"Now he'll have another full week's training and the risk element of a hamstring reoccurring starts to negate a little bit the longer it goes on. We're pleased because two weeks is a very short time for someone to be coming back.
"[Zabaleta has] gone over on his ankle. We don't have another game for another week now and we will have a look at it in the morning but I'd be surprised if he's out next week."
Fulham manager Martin Jol refuted claims that left back John Arne Riise had refused to play, stating that he was unhappy with the player's performance against Liverpool, and felt that Kieran Richardson's recent displays earned him a place in the team.
"John Arne Riise is a fantastic boy so he would never come up with that sort of crap," Jol stated. "I feel that he's a left back and I don't think that we've got Briggs, who's younger and who can go on the bench.
"John Arne Riise stayed at Motspur Park to do extra sessions because I promised him if he's not starting then it's probably better for him not to come with us. I always have to make a decision over two defenders and Briggs played over the last couple of games.
"Kieran Richardson was probably our best player over the last couple of matches, against Wigan he was our best player. I wasn't happy after the Liverpool game for example when [Stewart] Downing scored his first goal since he joined Liverpool and John was playing against him.
"I'm trying to do something, to freshen things up and alert John to do more and do better. I want to challenge all the players, Philippe Senderos played in the last game, I want to do something about the competition for places.
"John is different, he's an experienced player so if he's not playing he’s not happy. He wants to play but I've got three left-backs now and I think Kieran probably did the best job out of the three."
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