The Serie A club secured the last European spot on Sunday with victory over Livorno as fellow hopefuls Torino could only draw with Fiorentina.
However, Parma were not on the list of clubs with a license to compete in continental action released by the FIGC on Monday, amid allegations of unpaid income tax.
Torino have been issued a license and, if Parma's appeal to the High Court of the National Olympic Committee later this month fails, will likely take their place in European football's second-tier club competition.
Sporting director Pietro Leonardi explained the club's actions in a statement on the club's official website, revealing the matter came down to money spent by Parma to help other side's pay players' wages.
He said: "We were wrong, according to the FIGC commission, because we have 10 licensed players in another company with an incentive to sell.
"I make a concrete example with numbers: If a player earns €100,000 and the team that paid him, only €80,000 can be seen, Parma will give you the remaining €20,000.
"June 30, 2014 was the date that these guys would have to pay the difference but, for the sake of the kids themselves, with generosity we gave financial advances periodically on which, according to the FIGC, we would have to pay income tax.
"While, as also repeatedly assured by our tax experts, this must be paid in full at the end of June 30, 2014.
"The contradiction? If we had not paid, there would have been problems.
"We should not take part in the Europa League for a reason like that?
"It is because of this contradiction that we will remain quiet and confident. According to the commission, in essence, it is to all intents (a) salary payment or advance payment.
"It is a very good natured effect of common sense, and we want the decision to be changed. The players concerned are not in our payroll but another club's."
