The France international was slammed for his performance in the 1-1 Premier League draw, having given away a penalty for the opening goal at Old Trafford on Sunday.
"He is really important for us. He's great in midfield, good in the dressing room. He's an amazing player," the Spain goalkeeper told Sky Sports.
"At the beginning when you don't know the country, the players and the football it's a bit difficult. But you have fight, train more and try to focus and have belief in yourself.
"At the beginning it was difficult for me. With new football, new players and a new language everything was hard. But I kept believing in myself and kept fighting.
"In this country, in any country, you can make mistakes. We are humans. It is normal for a goalkeeper and players to make mistakes."
Despite falling behind to James Milner's penalty, United fought back to earn a point and extend their unbeaten run in all competitions to 16 matches.
De Gea, whose team visits Stoke City on Saturday, is eager to see Jose Mourinho's side continue their strong recent form.
"We want to keep winning," he said.
"We are in a good run and we need to stay at the same level, try to win many games and then we can see where we finish in the league."