The defending champions have opened up a five-point lead over second placed Chelsea and are hoping to seal back-to-back titles for the first time since they won the league three seasons in a row from 1999-2001.
"Winning the league again really proves what a good team you are," Carrick told the Daily Mirror.
"To win it on a one-off is a great achievement in itself, but if you can go two or maybe three years on the bounce then you are talking great teams.
"To win the Champions League is a dream and we're giving everything we can to do that, but to win the league twice is what great teams are made of.
"For winning the Champions League you go down in history and people remember you that little bit more, but for me the league is still very strong."