The Chinese businessman criticised official Jeremy Simpson after Villa’s 1-0 win over Bolton last month and has admitted an FA misconduct charge.
Xia wrote: “Is the ref a AVhater? Not our day but 3points only matters. Need keep going after the break. Consistency is the key this season.”
But the FA took a dim view and hit Xia with a fine and a warning.
A statement read: “Tony Xia has been fined £4,000 and warned as to his future conduct after admitting an FA misconduct charge.
“The Aston Villa owner and chairman made comments via social media on Saturday 30 September 2017, which constituted improper conduct in that they questioned the integrity of the match official and/or alleged and/or implied bias on the part of the match official, and/or brought the game into disrepute, contrary to FA Rule E3(1).
“The matter was heard before an Independent Regulatory Commission.”