James starred in United's somewhat surprising 2-1 victory over their local rivals, thanks to goals by Marcus Rashford and Anthony Martial.
Schmeichel told Premier League Productions: "He was unbelievable, chasing every ball, he was in every counter-attack and, at the same time, he was doubling up with (Aaron) Wan-Bissaka on the right-hand side.
"Ryan Giggs must be so happy to see one of his players perform so well.
"He's played every single game this season and he's still playing well. That's a fantastic signing."