The midfielder has admitted his side are not closing games as out as well as previous campaigns and it is a concern after losing the league on goal difference last season
United lost the title on goal difference to rivals Manchester City last season and the midfielder has urged his side to kill the game off like they have done in previous campaigns.
Carrick told reporters: "It has been a while. We had a spell, about a year or two ago, when we were starting games really well and killing teams off really early.
"We want to get back to that, because Old Trafford is a difficult place to play when you go a goal down.
"We want to make it that way, certainly in the games that are to come because going a goal down has made things a lot harder for us than they should have been.
"Keeping a clean sheet gives us something to build on in the future."
This was only their fourth clean sheet this season and after missing out on the Premier League title on goal difference last season, it is something United have to address as it appears to be a two-horse race for the title already.
Sir Alex Ferguson's men are a point clear of rivals City, and seven points clear of third-placed Chelsea. With that in mind, Carrick wants his side to become harder to beat.
He added: "Obviously we weren't at our best and the flowing football that you want to play and the chances that you want to create didn't quite happen.
"But we got a clean sheet, which was quite pleasing, and I thought we defended well. They had a couple of opportunities and when they put balls into the box like they did, those can fall to anybody.
"We got the clean sheet. It is something to build on because the performance needs to be better.
"A second goal would've put us in a much better position going into the final few minutes but, in the end, we held on and we're still in a good position at the top of the league."
Jonny Evans shared the same sentiments as his team-mate and has admitted that United did not play well and that they were fortunate to score when they did.
He said: "We didn't play well. The game was a bit slow and laboured. It was fortunate that we got the goal early doors but we didn't really kick on from that.
"I was thinking at the time, 'This is great, we've got a goal early doors and we can score a lot here', because everybody is looking at the goal difference, especially after what happened last season.
"I think we all know we didn't play to our usual standards. We'd had a tough game at the weekend [against QPR] or at least we made it tough for ourselves.
"It was quite a physical game, a lot of running was done and it was probably one of our highest running stats of the season.
"So there were some tired legs in the squad and I think it was all about seeing it out to get the three points.
"The clean sheet is good for the confidence, even if we didn't play in the normal United way. We probably were a bit more cautious going forward and holding our positions a bit more."