"The history of the club is something that is constantly breathing down your neck when you're a United player," Schmeichel told ManUtd.com. "That history and the expectation level makes you go that one step further than any other player at any other club in the world.
"When I first joined, the history we had to deal with was the Busby Babes, 1968 and the fact that we hadn't won the title for over 20 years. The desperation to win it was incredible and we all felt that.
"The current squad did brilliantly to win it last season and they have a great chance to go on to big things, but they have history on their shoulders as well because they have '99 to contend with which is a hell of a year to compete with.
"So, of course, the manager has got to go out there and say they're the best squad he's had. He has to make the players believe that and that's a good way of doing it.
"He's said it in the past when I was there and after I left. What he's basically saying is I'm extremely happy with what I've got and I love to work with these players. That's exactly what they need to hear and what the fans need to hear. If Sir Alex is happy United will win matches which is the most important thing."
The great Dane added: "The fact that Sir Alex has only won one European Cup is definitely something that niggles him.
"There's no reason why he couldn't have won a second one, but once you get down to the last four like United did last season it becomes a lottery. And things just haven't gone their way at the important times in the important games.
"They have a great chance to win the Champions League every season and I'd love to see them do it this time round."