Mourinho has come under pressure after a poor start to the season, but United bounced back with a 2-0 win over Burnley at Turf Moor on Sunday.
Schmeichel believes Mourinho still requires “time and patience” in order to bring the Premier League title back to Old Trafford.
“He’s been at great clubs,” Schmeichel told Sky Sports. “Real Madrid, Inter Mi-lan. He won the Champions League with Porto. Three Premier League titles with Chelsea. He’s done so many great things in football.
“But Manchester United is a different level to anything. The scrutiny, the tradi-tions and the history that we have. This is in the equation every day. Every single day, we respect our history. We have very proud traditions.
“We finished runners-up last season from fifth the campaign before. We’re straight into the Champions League this year, we won the Europa League and we’ve been in two FA Cup finals.
“This is great. Yes we strive for more, but these are very positive things.
“When we give him time and patience, when we understand this is a period in which we have to develop, we can win the Premier League.”
He added: “You can’t just walk into Old Trafford and you’re there. There’s so much to get used to. He must think ‘wow this place is so special’ because of what happens around him.
“Every single place that he goes, he will not meet one or two United fans, but big numbers. They live and breathe Man United. This is what the other clubs don’t have in those kind of numbers.
“There is nowhere he can go where Man United is not with him. I think that takes time. When I arrived at the club, I was surprised, and it took a long time to get used to.
“That was in 1991 and the club has grown since then. It’s different today. All over the world; South America, Asia and everywhere I travel it’s full of people who love the club.”
