Even after Pirlo he had Marchisio sitting behind him who is an experienced, intelligent CM with a good passing game. Pogba needs a player that not only provides a defensive net behind him, but one that can consistently feed the ball to him so he can stay higher up the pitch.
I wasn't referring to Bakayoko in that regard, he's not a DM, he's a box to box CM the same as Ander, the one that sits deep for Monaco is Fabinho. The key component missing when you take Carrick out is not a physical one, but a brain to orchestrate that midfield.