The duo made more than 800 appearances for the club between them and have voiced concerns over United's apparent decline, with the defending champions having lost as many Premier League games this season as they did in the entirety of the last campaign.
Keane spoke out at half-time of United's 1-0 UEFA Champions League victory over Shakhtar Donetsk, suggesting that Moyes' side were failing to press the opposition or make tackles, with Rio Ferdinand and Ashley Young bearing the brunt of his ire.
Ex-goalkeeper Schmeichel, meanwhile, has urged Moyes to get rid of his underperforming players in order to stamp his authority on the squad.
Moyes, whose side travel to Aston Villa on Sunday, readily accepted that the Old Trafford legends had made some valid points.
"Some of what they're saying is correct," the Scot said.
"There's some of it that's not correct because it's certainly not the (United players') attitude or effort because they're really trying.
"I can only tell you every time we've played a game we haven't won, the players have been distraught by it and there's been a real toughness in them to try to put it right."
It was Alex Ferguson who brought Keane and Schmeichel to the club and the Irishman has claimed Moyes' predecessor still has an influence on first-team matters - a notion the current boss rejects.
"I can pick up the phone to him when I need to, which I do now and again," Moyes explained. "Obviously we bump into each other because he's a director; we say hello after the games.
"He doesn't (come to the dressing room). A lot of the directors do but Alex keeps away from it."
