The Ducale club beat Torino in the race to finish sixth in Serie A to clinch the final European qualifying place.
However, the Gialloblu outfit have not been granted a UEFA licence by the Italian Football Federation (FIGC) due to financial irregularities.
"Parma is confident that it will obtain the UEFA licence," Parma sporting and managing director Pietro Leonardi said on the club's official website.
"We will have to appeal to the high court of CONI (Italian Olympic Committee). But I am calm."
Parma have already had their UEFA licence twice rejected by the Italian football bosses due to a dispute over income tax on their contracted players that have played on loan at other clubs this season.
"We have 10 players on loan at other clubs," Leonardi said.
"If a player earns 100,000 euros and the team that he is loaned to only pays him 80,000 euros, we have to come up with the remaining 20,000.
"June 30, 2014, was the date set to pay these players that difference.
"But in the best interest of the players, we decided showing generosity, to anticipate the amount with periodic payments.
"According to the FIGC, we should have paid income tax on that.
"However, our accountants believe this should be paid on June 30, 2014 on the deadline day of the final balance.
"Although we didn't agree with their (FIGC) interpretation, we went ahead and paid the 300,000 euros requested one hour after the first hearing.
"Are we not going to compete in the Europa League because of this? It's an issue of interpretation.
"We have had to sweat to clinch sixth spot and no-one can say otherwise."
Clubs must have a UEFA licence to compete in Europe.
Parma, coached by Roberto Donadoni, have until May 28 to make a final application, which would be reviewed by CONI's High Court of Justice.