United made it seven wins from eight matches by beating Newcastle United on Boxing Day but remain 10 points behind Chelsea and seven shy of second-place Manchester City.
While many of the Old Trafford faithful believe a Champions League place is a more realistic aim, Carrick is not giving up hope of a 21st Premier League crown.
"We're continuing to look up and will continue to try to catch them [City and Chelsea]," Carrick told United's website.
"We're not satisfied with third. It's obviously an improvement and we're getting better but we want to keep looking up."
On Boxing Day, United boss started with an attacking quartet of Wayne Rooney, Radamel Falcao, Juan Mata and Robin van Persie and it is such firepower that is giving Carrick renewed cause for optimism.
"That's four world-class players you're talking about there," he said.
"Going in to a game with those lads in your team gives us a real threat and a lot of confidence knowing we can create chances and score goals. Against Newcastle they clicked nicely and hopefully in the weeks coming up we'll see something similar."
United travel to Carrick's former club on Sunday, and the midfilder added: "Going to Tottenham is always a tough game and to go there two days after this match at 12 noon makes it very tough.
"But we have to get ourselves ready for that and it's the same for them as well. It's a game we look forward to and we go there confident."
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