Gaucci said he would no longer employ Ahn, whose 'golden goal' dumped Italy out of the World Cup in the second round.
"It's a childish reaction," Korea coach Hiddink said on Thursday.
"
I feel offended by what he said - he should respect other nations as well as
his own
"
Perugia president Luciano Gaucci
"Sports means players are all playing in different countries."
"Do they say to Frank Leboeuf and Marcel Desailly, they cannot score against England from the corner kick? It's almost too ridiculous to talk about."
Gaucci has indicated that his club's decision to sack Ahn was prompted not by his goal but by his remarks afterwards, which were "offensive to me and the whole Italian nation.
"It has nothing to do with the goal he scored against Italy," said Gaucci.
"He could have scored 10 and I wouldn't have felt offended. It was simply the comments he made."
"He said Korean football was superior to Italian football, when Italy is a footballing nation.
"We have treated him well with all our love, but his comments were offensive to me and to the whole Italian nation.
"I feel offended by what he said. He should respect other nations as well as his own."
Ahn missed a penalty during the first half of Korea's 2-1 win over Italy on Tuesday, but was hailed as a national hero when his 116th-minute header set up a quarter-final with Spain.
Gaucci told Italian sports daily La Gazzetta dello Sport: "That gentleman will 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.
"I have no intention of paying a salary to someone who has ruined Italian soccer."
However, Perugia coach Serse Cosmi added another twist to the tale by declaring he would like Ahn to stay at the club and urged Gaucci to reconsider.
"I consider him a player with enormous potential," Cosmi said. "I wouldn't have any objection at all if the club decided to extend his contract for next season."
Fifa, meanwhile, refused to "interfere" with the decision to dismiss Ahn.
"It's between the player and the club," Fifa communications director Keith Cooper said.
"It's not for us to interfere. No-one has complained to us."
Ahn Jung-Hwan joined Perugia on loan from the South Korean team Pusan Icons in the summer of 2000, but he scored just five goals in 29 appearances.
Even before scoring his famous goal, Ahn, with his model looks, was a huge celebrity, the closest thing the Koreans have to David Beckham.
He is married to a former Miss Korea, Lee Hye-Won.