Villa beat West Brom 2-0 in March and have now reached the final against Arsenal at Wembley on May 30.
"The club was charged for failing to ensure that no spectators or unauthorised persons were permitted to encroach onto the pitch area whilst attending the game at Villa Park," the FA said in a statement.
Villa have also been "severely warned" as to their future conduct.
(Reporting by Toby Davis; editing by Justin Palmer)
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