Ji, 22, played four matches before the Wearside club realised they had failed to gain an international clearance for the striker, who returned to England after a loan stint with Bundesliga outfit Augsburg.
The club confirmed the error was an administrative one, and they had already paid the fine to the league earlier this year.
"There was an administrative issue regarding the registration of the player," said a club statement released to ITV.
"The club was fined by the Premier League and the matter was dealt with at the time."
Ji also played in the Capital One Cup, a tournament the Black Cats went on to reach the final in, and they also paid a fine to the Football League for his involvement in a tie with MK Dons.
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