Carrick says his players are well aware of the rivalry and what is expected when they host Leeds at Old Trafford on Monday.
He said, "It's gone on for an awful long time. I think that's what rivalries are there for, for a really good reason, I think, to be part of, and the intensity and the emotion and the passion that goes into it. Obviously, it's got to keep within the margins, but I think that's part of the game we love, going up against other teams, essentially all the areas, you know, and battling it out on the pitch.
"So I think it's something that we've got to embrace. And it's, as I say, it's why we were involved for these type of games. And we're certainly aware of it. I'm certainly aware of it. The players are aware of it. The extra that it means on top of the standard three points. So, yeah, we're looking forward to it. It's a big night for us.
"Hopefully it cranks it up (the atmosphere), you know, and the stadium is alive.
"I'm sure it will be. It has been. It's been unbelievable playing at home and the boys have responded and thrived off it, really. So, and with the supporters giving, you know, that balance and coming with us and, spurring us on when we've needed that. So I expect it to be the same and with an extra little bit of edge because of it being late."
With former Leeds defender Jonathan Woodgate now on his staff, Carrick was also asked if Woodgate had discussed the rivarly with the players.
"Not loads, actually. I think we're all aware of what the game means to the football club, to the supporters. And, yeah, just kind of repeating what I'm saying.
"I think it's something you've got to thrive on and understand when you play certain games what it means for the wider picture. It's for so many people in different ways. Sometimes it's what you'd call a normal game, sometimes it's a little bit of a twist to it, and this is certainly one of them."