United intend to focus their summer business on two midfielders, a left-sided player and a forward. They have five specialist centre-backs, with Matthijs de Ligt, Lisandro Martínez, Leny Yoro, Harry Maguire and Ayden Heaven all contracted at the club.
Carrick was measured in his assessment when asked about the position.
"It's not an area of concern for me at this moment in time. I think we've got a mixed blend there of experience, of real quality and some young — I'd say more than talented really — two promising young players that have already shown what they can do. I thought Ayden was fantastic last week in such a difficult game. I haven't got concerns."
De Ligt has been sidelined since November with a back problem and has not undergone surgery. He has returned to outdoor training in a limited capacity.
Carrick gave a carefully worded update.
"Matthijs is working towards being fit again. He's doing a little bit on the grass and it's progress. He's back on the grass at the moment, in a small capacity, but he's working towards it. So that's positive. We're all hoping that it keeps going in that direction."
He declined to offer assurances about De Ligt's future, given the uncertainty around his own position.
"I think it's difficult for me to sit here and make judgements and comment on that. We just want him to get back fit."
Martínez is serving a three-match ban following his red card against Leeds. Maguire signed a one-year contract extension earlier this month.