As the squad prepared to leave South Korea today, local media said players refused to sign autographs for fans at the airport.
Meanwhile Perugia's Gaucci told sports daily La Gazzetta dello Sport that Ahn would never set foot in Perugia again.
"He was a phenomenon only when he played against Italy. I am a nationalist and I regard such behaviour not only as an affront to Italian pride but also an offence to a country which two years ago opened its doors to him," he said.
"I have no intention of paying a salary to someone who has ruined Italian soccer."
Ahn has been on loan to Perugia, who finished mid-table in Serie A last season, from South Korean club side Pusan I.cons since 2000, but has struggled to hold down a regular place in the team.
Even before the win over Italy, media reports had suggested that Ahn would be released by Perugia, with English and German clubs among those interested in signing him.