Van Persie claimed the only goal today, although replays suggested his shot was not going in until Titus Bramble put it into his own net, but the striker was not too concerned.
"We got the three points, we knew it would be tough because Sunderland work hard and we had to dig in, but we deserved it," he told Sky Sports 2.
"It didn't matter who scored today, it was all about the three points.
"This team is full of winners, everyone knows what they have to do and it was never in doubt for me. I was confident we would win."
A title coronation seems inevitable in the next couple of weeks and midfielder Carrick is anticipating winning another medal.
"We played some good football today, even if we didn't get as many goalscoring opportunities as we'd have liked," he added.
"It was all about coming here and winning. We're getting closer and it's one game less. We have to keep going."