Three points against Chelsea on Monday night would certainly be a big boost to the title defence, particularly with visits to Liverpool and City coming up early next month.
"It was a good start for us [at Swansea] and important to get off to a win given the whole picture in terms of having a change in manager and a tough start to the season in the first five or six games," added Carrick. "It was a decent performance but there is still an awful lot of improvement we can make and more to come from us.
"Sir Alex said a few years ago about how you used to be able to almost start slowly and then come Christmas really gain momentum until the end of the season. But now, because whichever team wins the league doesn't lose many games or drop many points, you have to be right at it. There has been a real emphasis on that in the last few years. It's something we're all aware of and other teams are aware of too.
"It's tough to know [which teams will be involved until May]. Two years ago Tottenham were right in there, but they faded a way a bit. I think there potentially could be four, five or six teams involved right until January or February. Just after that is when it really gets sorted out and when the pressure kicks in and the expectations change. It's how you deal with that. Hopefully we'll be right in there with a shout by then and we can use our experience to see us through."