An SFA spokesman said: "The Scottish FA is apologising to Uefa and the Italian FA for this rules infringement, as well as to the player and his club."
Scotland had no chance of qualifying for the European Under-21 Championship despite Friday's thrilling draw with group leaders Italy.
Whittaker was under suspension after picking up two yellow cards against Moldova and Belarus and should not have played.
He will not be selected for the match against Norway on Tuesday.
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