Black Cats supporters revelled in Manchester City's title triumph at United's expense on the final day of last season, but Carrick says the Reds' sights are set to the future.
"They weren't the only fans who enjoyed that, but that was gone and it was all about coming here with something different to aim for this time," the midfielder told Sky Sports.
"It was about getting points for us, ticking another one off and keeping the run going, which we did, and we're delighted."
United's victory at the Stadium of Light owed more to defensive fortitude than attacking guile, and Carrick was heartened to see United grafting three points closer to the title.
"We played some very good football first half, controlled the game," he said. "We probably didn't have as many goalscoring opportunities as we'd have liked but we were in control.
"We knew the second half was going to be different because they're fighting for their lives. We defended well, kept together, defended our goal well and we're delighted with the three points.
"I suppose we're getting closer because it's one game less and we've won again, but that's all it is. We've still got to go again. We've got another game on Monday and then obviously City next week, so we'll keep rolling on."