The result sees United second in the table, three points behind Liverpool.
"Yeah, I feel very confident, to be honest," De Gea said. "I feel well. I am happy every time I can help the team like today, make some big saves to keep the clean sheets. The whole team I think we played a good game so, yeah, I'm really happy.
"We have a big squad. We trust in every player. If we make changes it's because we believe in our players. The whole squad is ready to play so it's really good to see when players play one game, play well, then rest, then they play again. It's beautiful to see how players are ready to play.
"Of course, I think there's belief," he added of the mood inside the dressing room. "You have to believe, keep believing all the time.
"But at the same time we have to be calm because this is a long way to finish, many games to come. We have to be very focused on Aston Villa and then to the next game and then to the next game."