The Netherlands international joined United from Arsenal earlier this month and scored on his home debut in their 3-2 victory over Fulham in the league.
"I'm very excited about the season ahead," said Schmeichel in his club ambassador's column for 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."
However, the 48-year-old has warned United not to get complacent.
"Of course, while things may look very good on paper, lessons must be learned from last season and the players need to go out and do the business," said Schmeichel.
"But there is no question we have the personnel to win the title back."
United are back in Premier League action on Sunday when they take on Southampton away from home.