The 31-year-old, handed the suspension last month after failing a doping test, challenged the severity of the punishment but has failed in his efforts to have it reduced.
In a statement to Sky Sports News, Kenny said: "I am devastated that an honest mistake on my part could cost me my career.
"I would like to thank Sheffield United - plus all my current and former team-mates, as well as my agent - for their support throughout.
"I am positive I will bounce back, and I really hope that this experience will stop others from making the same mistake."
Kenny was handed the ban after a routine urine sample taken following the Blades' Championship play-off semi-final clash with Preston in May was found to contain traces of the banned substance ephedrine.
He was suspended by his club in June and then by the FA the following month, and his punishment was handed down after a regulatory commission hearing last month.
Kenny, who admitted the charge, told the commission he had taken tablets bought at a chemists to help with a chest infection before the Preston game.
He was cleared of cheating but banned from playing for nine months, back-dated to July 22, the day the FA's suspension came into force.
Kenny's representatives, with the backing of the Professional Footballers' Association, argued at Tuesday's hearing the sanction was disproportionate - because he had not used the medicine to enhance performance.
However, an FA statement said: "The appeal board dismissed the appeal by Mr Paddy Kenny against his nine-month suspension for a breach of the FA doping regulations.
"The regulatory commission's decision to impose a nine-month suspension was an appropriate measure of the seriousness of the offence."
Responding to the decision, Blades boss Kevin Blackwell told his club's official website: "We are very surprised by the outcome.
At this stage, we do not understand why it has been decided."