The Lilywhites won 2-0 at Vale Park despite Australian midfielder Kilkenny, who is on loan from Bristol City, being shown a red card in the 13th minute.
Preston released a statement on their official website that they plan to appeal the decision: "Preston North End are intending to appeal the red card handed out to Neil Kilkenny in Tuesday's victory over Port Vale.
"The Club intend to appeal the sending off on the grounds of mistaken identity, following an incident which occurred in the 13th minute of the 2-0 win over the Valiants."
The match was Kilkenny's third appearance for the Lilywhites since crossing from Bristol on a one-month loan on November 14.
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