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The Spanish international, who joined the club in 2011, kept a clean sheet on his 399th appearance for United on Thursday as Ole Gunnar Solskjaer's side won 3-0 at relegation-threatened Aston Villa.
"Sorry to Schmeichel," he told mufc.com. "It's great. That means I've been here a long time and I've been playing really, really well to the top level so I'm really, really proud. I'm happy to play for this club for that many games.
"Hopefully I have another 400 games coming. So I'm really, really happy."
Solskjaer's team - unbeaten in 17 games in all competitions - moved to within one point of the Premier League's top four after goals from Bruno Fernandes, Mason Greenwood and Paul Pogba.
Fifth-placed United are a point behind Leicester, who they face on the final day of the season, and two adrift of Chelsea as they bid to return to the Champions League.
But with four games remaining De Gea, 29, said the job needed to be completed.
"Of course we are very confident now but we haven't done anything yet," the goalkeeper said.
"We have some important games coming now so we need to be very, very focused and keep the level that we showed today and in the last four games."
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