The Spaniard insists Nani's 'unfair' red card let Real come from behind and win 2-1 at Old Trafford earlier this month.
De Gea revealed: "Sir Alex has a lot of character and on that day he was very angry, although deep down what he felt more was pride for his team.
"We were superior to Madrid and deserved more but there were situations - unfair decisions and we were knocked out.
"Football is like that and in that type of game details leave you knocked out. The expulsion of Nani marked the game and the tie. Without that red card it would be Manchester United in the quarter-finals."