Casemiro opened the scoring against Brentford with a header and was dominant in midfield throughout, his work rate and physicality providing the platform for United's 2-1 win that consolidated their third-place position.
"It's pretty clear how much it means to him," Carrick told his post-match press conference. "Probably the situation, the clarity of it, has helped everything. It means a lot to him and credit to him because he's giving absolutely everything and he's had some big moments for us. All round, it's quite a nice direction for it to be taking."
He was asked about maximising Casemiro's presence in the dressing room through the final games.
"Case has had an influence within the group. He's got huge experience. He's a big player who has achieved an awful lot in the game. Since I've arrived, he's given everything he could possibly give.
"The situation has probably helped that — knowing exactly where he's at. He's got nothing to hide. He's thrown himself right into it. It's football, players come and go. You've got to evolve and move on and adapt. That's the world that we're in.
"It's nice that he's got that connection with the supporters and it comes from both ways because I know he's an emotional guy and it means a lot to him."
Casemiro will leave when his contract expires in June. Kobbie Mainoo has been Carrick's preferred midfield partner for the Brazilian through the run-in.