The victory means they are just six points adrift of the top, but with a game in hand.
They also have the prospect of a much easier second half of the season in which they will face all their title challengers at Old Trafford.
Midfielder Carrick has only known success since moving to United for £18m in 2006, winning two titles and the Champions League and he has no doubts he can make it a hat-trick of titles, even if Sir Alex Ferguson's side are in the unusual position of being one of the chasing pack.
"It's a tough challenge to win the league any way, we've done it from in front before, so we'll try to do it from behind. That's what it's all about. It's always a challenge. We want to keep the run going that we started. We're playing pretty good stuff - it's just a case of things not dropping for us at times. But a win is a win and we can move on now. There is a growing sense that United's title challenge is gathering momentum, having picked up 10 points from a possible 12 since defeat to Arsenal last month.
With Liverpool and Chelsea faltering in recent weeks, it has allowed Ferguson's side to close the gap at the top and leave them poised for a concerted charge in the New Year.
Carrick continued: "Even without Liverpool, Chelsea and Arsenal winning, it was important we won the game, it was very late, but I think we deserved a win, you can't argue about that. The way it came was very exciting, but we should have killed it off a lot earlier than that. Everyone will do well to go the rest of the season without dropping points, it is a case of who can be the most consistent. We feel we've got the right players to do it, but only time will tell. We believe we are capable of winning the league for certain." .....Back To Home Page...