Carroll, now with Olympiacos, feels De Gea has responded to Ferguson's guidance.
He told talkSPORT: "I think he's kept his head this season. I've watched him and he's made some fantastic saves and nobody has really talked about them.
"You have to believe in your keeper and I think Ferguson does believe in him.
"That's what you want as a goalkeeper, that the manager trusts you.
"I think Ferguson speaks to him and I think he's done it a lot this season and it's telling from his performances over the past months."