The Spanish shot-stopper has faced widespread criticism since moving to Old Trafford from Atletico Madrid in 2011, with it suggested that he makes too many mistakes to be a top-class keeper.
De Gea is still only 22, though, and is developing his game under the brightest of spotlights.
His performance against Real Madrid in the UEFA Champions League on Wednesday, as he helped United to a 1-1 draw at Santiago Bernabeu, suggests he is paying little attention to his detractors, and Carrick insists the youngster has the full backing of those inside the United camp.
The England midfielder said: "There is no bigger pressure cooker really than this stage of the Champions League and coming to a place like the Bernabeu.
"He was coming back home as well, so there was an extra spotlight on him.
"Some of his saves kept us in the games at times. It just showed what he is all about."
Carrick added: "It is never nice when people question you but that is natural at a club like Manchester United. You are always getting questioned and criticised. That is just how it is. That is fine. You have to deal with it.
"He is a top keeper and he is only going to get better. To play at this club at such a young age and have so much on your shoulders, says enough on its own."
Carrick has also offered support to Danny Welbeck, with the striker grabbing just his second goal of the season in Madrid.
He added: "Danny was magnificent. He has all the attributes to be a top player but probably doesn't get the credit he deserves.
"If the team is winning, who is scoring is not such an issue.
"As a Manchester lad, he loves the place. He is genuine and gives everything. He worked so hard again and I am delighted for him."
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