Chelsea host injury-hit United in the FA Cup quarter-finals on Monday, five months on from their 4-0 top-flight victory over Jose Mourinho's side.
Carrick insists the occasion is not about a chance for revenge, but feels the gap has been vastly reduced since their last visit to Stamford Bridge.
"You can't say we have got a score to settle," Carrick told reporters ahead of a game which is expected to see United without Anthony Martial, Marcus Rashford and Wayne Rooney as well as the suspended Zlatan Ibrahimoivc.
"There is plenty has happened over the years so it is just a new game and a chance for us to go further in the competition and they will say the same.
"We have lost only one in 28 games now since that Chelsea defeat so we have had a good run of form.
"They have gone on a great run so you have got to respect what they have done. It is not easy in this league to go on such a run.
"We have gone on a good run ourselves but we have just had too many draws at home and that has killed us.
"We feel that we are getting closer but you have got to respect them, they are a good team, they are well drilled."
Carrick continued: "It is a massive game, a one-off game, so we are looking forward to it. We are in pretty good form ourselves and they are obviously having a great season so far in the Premier League.
"They have been able to field pretty much the same team all season which I think has helped them and they have not had European competition to worry about.
"But they still had to go out and get the results and they have done that so you have still got to respect them for that."