Moyes was unhappy with the match officials following the 2-1 defeat - United's third consecutive loss - particularly Andre Marriner's decision to award a free kick to Sunderland which resulted in their opening goal.
"We've got an opposition to play and sometimes we've got other people to play at the moment," Moyes was quoted as saying after the first leg defeat.
Charging Moyes, the FA alleged the comments "called into question the integrity of the match officials".
"Moyes has until 1800 GMT on January 15 to respond to the charge," the FA said.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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