However, Schmeichel believes that Hart has been harshly treated, both by Pellegrini and the British press.
"I don't think he's done too much wrong," Schmeichel told BBC Sport. "Sometimes things aren't working for you, but when it's Joe Hart it's highlighted like he's killed someone.
"I disagree with Pellegrini's decision. I disagree with the whole debate about Joe Hart. He might have had the odd situation, but he hasn't gone from being an absolutely brilliant keeper to what he is being portrayed as now.
"Why is it that when you finally have an English goalkeeper who has the quality to become the first part of the spine that can actually take England somewhere, everyone wants to drag this kid down? You have a unique goalkeeper here, someone who is very, very good even on his bad days."
Hart has been capped 37 times at senior international level.