Villa, who booked their place in the final with a 2-1 win over Liverpool at Wembley on Sunday, are accused of failing to ensure spectators did not enter the field of play during their 2-0 win over West Brom at Villa Park.
Reading, meanwhile, face the same charge in relation to their 3-0 replay victory over Bradford City.
Steve Clarke's men were beaten 2-1 after extra-time by Arsenal on Saturday, with Adam Federici conceding the softest of Alexis Sanchez goals in the first additional period.
Both clubs have until Thursday to respond to the charges.
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