"I feel very sorry for him," Carroll told BBC Radio 5 live.
"You need the manager's backing and I think he's got that because he's played a lot of games since he's come in."
Northern Irishman Carroll, 35, who now plays for Olympiakos in Greece, said: "He's a very good keeper. He's still young.
"There have been a lot of changes at Manchester United across the back four this season with injuries so I think it's very difficult for him at the moment."
Carroll, who joined United from Wigan in 2001, continued: "I had four years there but I made a lot of mistakes as well.
"Once you make mistakes, people just never forget about it so I think as a young goalkeeper it's very hard.
The latest criticism for De Gea came after he failed to punch clear in the lead-up to Tottenham's equalising goal in Sunday's 1-1 draw with United.
Carroll said: "I think he had a decent game against Spurs but the goal came from a cross.
"You have to be a lot stronger from crosses. I think he knows that himself. His shot stopping is fantastic but he knows he has to work harder from crosses."