The outgoing champions have suffered six defeats in front of their own supporters in the top flight as their title defence faltered badly under new manager David Moyes.
But the Red Devils have reached the quarter-finals of the Champions League and drew 1-1 at home to holders Bayern Munich on Tuesday night in the first leg of their last-eight clash to maintain their hopes of progress.
Recent home defeats at the hands of Manchester City and Liverpool were particularly galling for goalkeeper De Gea and his team-mates.
And while the Spaniard admitted the setbacks demanded a response, he is unsure why there is a disparity between their domestic and continental displays.
De Gea said: "It's hard to say why. There's no particular reason for it.
"But we've certainly played better and been more consistent in Europe than in the league.
"They're two different competitions and things haven't gone well in the league, but the Champions League is a special competition, the team have done well.
"It's been quite a tough period for us in the league and we were down after the defeats to Liverpool and (Manchester) City.
"But we are United and we must lift ourselves and fight.
"This is a big club and at difficult moments is when you stand up and show people how big you are."