The Spain International gave the warning ahead of Man United’s game against Arsenal on Thursday.
The goalkeeper said the players must raise their game to beat an ‘improving’ Arsenal.
Manchester United won one and drew one of their last two games under caretaker manager, Michael Carrick who has now been replaced by Rangnick.
The club announced the arrival of Rangnick on Monday a few hours after the 1-1 draw against Chelsea at Stamford Bridge.
The Red Devils host Arsenal at Old Trafford on Thursday, with the club looking for just their second victory in the league in their last eight outings.
“I think from today [the draw against Chelsea] we should take a lot of confidence,’ said De Gea, according to Metro.
“We know Arsenal are in a good moment, they play well, they are improving, so it’s going to be a big game.
“I think the spirit of the team was great, the fight, the determination, the desire – it was great.
“That should give us more confidence to win big games and to see again the team playing properly, scoring goals and winning points.
“We knew we had to not concede for at least the first 20-25 minutes. We defended quite well; aggressive. The players gave everything and it was good to see the players running all over the place, trying to play and trying to fight for the club.”