Manchester United's previous Premier League draw with Chelsea at home, De Gea said that the team's downturn at Old Trafford may be because there were no fans at the scene.
Manchester United have yet to taste a win in their three home games this season. In contrast, they have won all five away games.
De Gea said: "Why is our home state and away state so different? I don't know, maybe it's because of the fans, we miss them so much."
"We have to make sure to win the next home game at Old Trafford. We have not won three home games. So now is the time to start winning at Old Trafford. I think we are today. Deserving to win."
"It's great to get a clean sheet. We have conceded some goals in the past few games. Chelsea did not create many opportunities. We defended well and we have a great chance to win the game.