De Gea is currently in Israel with the Spain Under-21 team, who play Norway in the semi-finals of the European Championship as they seek to retain the title they won in 2011.
The Spaniard told AS: "I am very proud to have had the privilege of working with Ferguson, it was a real pleasure.
"He is the best coach of all time and it is something I will be able to tell my children and my grandchildren.
"The best advice that he gave me was to simply give my all," he added.
"He told me to continue with the same mentality I have always had. I owe a lot of my capabilities as a goalkeeper to him."
De Gea admitted it would take a while to get used to not having Ferguson around, but insisted he was looking forward to working with new United boss David Moyes, who he believes is similar to his former boss.
"It will be very strange because he spent 26 years at the same club, but this is football, and all eras must come to an end.
"We are delighted that Moyes is the new coach as he has the same level of enthusiasm as Ferguson."