The Dutch international signed for United earlier in the month and then scored on his home debut to help his new side beat Fulham 3-2.
"I'm very excited about the season ahead," said Schmeichel in United Review.
"And, for me, the signing of Robin van Persie is a real game-changer.
"By bringing Robin in, we've shown our intent for the season – we've got the one player everyone wanted and we got him because we can provide a fantastic platform for anyone who has ambitions of winning trophies.
"We have gone from being neck and neck with Manchester City to now, in my opinion, being ahead; our squad has greater depth than anyone else in the league."