While United have been inconsistent under Moyes's management, Martinez has guided the Toffees to fifth in the table, having lost just once.
"He is doing a very good job," Moyes told reporters. "He has very good players there.
"I always told them they could play without a manager because they are very well organised, but Roberto is doing a really good job keeping it going."
Moyes never won at Old Trafford during his 11-year tenure with the Merseysiders.