The Red Devils have opened up a commanding lead at the summit, and cemented that standing with a narrow 1-0 victory over Sunderland on Saturday.
An own goal from Titus Bramble saw them to three points on Wearside, but United were able to control the contest for long periods and have now collected seven straight wins in the league and six successive clean sheets.
Everything would appear to point towards them reclaiming the top-flight crown in 2012/13, but Carrick says no-one at Old Trafford is taking anything for granted.
He told Sky Sports: "We are getting closer because it's one game less and we have won again, but that's all it is. We have still got to go again, we have got a game on Monday and (Manchester) City next week, so we'll keep rolling on.
"It was about getting the points for us and ticking another one off and keeping the run going, which we did and we're delighted with that.
"I thought we played some really good football first half and controlled the game. We probably didn't create as many goal-scoring opportunities as we would have liked, but we felt in control.
"We knew the second half was going to be different because they are fighting for their lives. We didn't expect it to be easy, but we defended well, kept it together and are delighted with the three points."
Robin van Persie fired the shot which forced Bramble to put through his own net at the Stadium of Light, and the Dutch striker believes United's desire to be the best will see them to silverware this season.
He said: "We have got the three points. We knew before that it was going to be tough, Sunderland always work very hard and they play a game with a lot of long balls, second balls, and we had to dig in. We did that, everyone fought hard, and I thought it was a well-deserved win.
"This team is full of winners. Everyone here knows what they have to do. It was never in doubt. It was a small score, 1-0, but I was always confident that we would win this game because people like Mike (Carrick), Vida (Nemanja Vidic) and Chris (Smalling) have been playing really well. Alex (Buttner) just comes in and plays well. Everyone knows what they have to do."