Nani says the Reds missed a "great opportunity" to close the gap on Chelsea to just one point at the top of the Barclays Premier League.
The Reds drew 2-2 at Bolton on Sunday, a result United skipper Nemanja Vidic said he and his team-mates were viewing as two points dropped.
Before kick-off, Sir Alex's men lay four points behind Chelsea, who lost at Manchester City on Saturday. Perrenial title rivals Arsenal also suffered defeat on Saturday, losing 3-2 at home to West Bromwich Albion.
It meant a win at the Reebok Stadium would have taken the Reds to within a point of Carlo Ancelotti's side. But things didn't go to plan for United, who twice had to come from behind to draw.
"We’re disappointed because we wanted to win this game, especially because Chelsea and Arsenal dropped points," Nani told MUTV. "It was a great opportunity for us, but we drew. We want to fight for that top spot.
"Our rivals lost and this was a good chance to get closer to Chelsea but we still have a chance to get to the top of the league. We now have to look forward to the next game.