Schmeichel, who appeared 292 times under Sir Alex Ferguson, said Moyes was always going to face a rocky initiation.
"We always knew that whatever happened after Sir Alex, it would be a bumpy road," Schmeichel told Sky Sports News. "Someone had to be really brave and take that job.
"We knew every little thing that he does would be scrutinised and reported on in the media. It would be a debate - is he good enough?"