De Gea kept his place for victory at Newcastle United on Sunday.
He said: "I am working flat-out every day because I need to regain the confidence of the coach.
"For me, a training session is a match and after that it is necessary for me to show what levels I can achieve in games.
"I ended last season satisfied with my work for Manchester United, but it is quite normal to go back to zero at the start of the following season.
"I don't believe I have been at the top in the last couple of months but with each game I am rediscovering my level.
"I accept the manager's decision. If he considers Anders as No.1 it is not a problem for me I only want to problem for me and I only want to maintain my challenge for the position.
"I am young and it isn't easy to be the No.1 at United, even though that was the case last season. Now I just want to repeat that.
"I am confident enough to order around my team-mates, even though they are older than me. The manager says that, in the area, I am the boss!
"I always dreamed of succeeding at a club like United. From the moment I arrived, I knew that it wouldn't be easy. This is not a simple club. It has huge power and support all around the world."