United have made their worst start to a Premier League season in 12 years, taking just 22 points from their opening 15 games.
Schmeichel believes that personnel changes are needed at Old Trafford and that Moyes should have a clear-out in January to get rid of those individuals who are not committed to the cause.
"I think more than anything, he should let players go," Schmeichel told the Daily Mail. "There are some players in there that are not doing the job and haven't been doing the job for a bit now.
"To be a Manchester United player, it requires a certain level of performance, mentality and you have got to be proud to be a Manchester United player.
"I just see with five or six players that they don't care and we [United] have never ever had players that don't care. You should care."
Schmeichel added that playing for United is a huge responsibility that some players do not understand.
"It's so obvious," he said. "Everyone is talking about it. Let's say the club have 560m supporters. If you are named in the first XI, you carry the responsibility for 560m people's well-being at that time. That's a lot of people. There are 75,000 people there at Old Trafford every time you play a game.
"This is what you have to understand when you are a Manchester United player - this is the kind of responsibility you have to take on the pitch. Certain players look like they don't care and they should not be at Manchester United.
"I think David Moyes will already have identified that, and the statement that he will make by letting players go will be more powerful than the statement he will make by bringing players in."
United travel to Aston Villa on Sunday afternoon, when they will be aiming to record their sixth league win of the season.