Despite the long break between matches, United are not expected to be boosted by the return of players from injury. Carrick said that Mason Mount was closing in on making his return but would not be available for United's first game at the Hill Dickinson Stadium. Matthijs de Ligt, who has been missing since injury since November, is also still out.
Carrick was part of the United squad that floundered in David Moyes' solitary season in charge after succeeding Sir Alex Ferguson in 2013 but he said he had huge respect for the Everton boss.
He added: "David’s teams are hard to play against. He is such a good manager – the experience he has got, he knows what it takes to have success in this league. It is a new challenge for us and one we are looking forward to. We have had a lot of time to look forward to it. It is going to take a lot. I know it is a new stadium but historically it has always been tough going to Everton. The atmosphere their supporters create, it is always one of the toughest ones I have played in, so we are aware of that. We are trying to be our best. We have things to improve on but we have a good base and foundation moving forward. A good spirit and we will draw on pretty much all of that on Monday night."