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.