Carrick has returned after pulling out of the Euros campaign this summer.
"Michael is a fantastic player, one of the best I'll ever play with," said Cleverley.
"This country must have had some good midfielders if he's only won 22 caps.
"Sometimes you need to see it first-hand with Michael to realise how good he is.
"A lot of clubs have those players who are massively important but go under the radar a bit."