Rossi, who has just recovered from his latest knee injury, took part in a week's training and played Saturday's friendly against Ireland, only to be left out when coach Cesare Prandelli trimmed his provisional 30-man squad to the final 23 on Sunday. (Agencies)
Rossi poured scorn on suggestions that he was still not fully fit.
"Everyone is saying I'm out of shape: ask anyone the results of the tests from last week and from the match," said the American-born forward on Twitter on Monday.
"You will be surprised. Challenges? Fear? What a laugh," added Rossi, who is probably Italy's most reliable forward when fully fit.
"The most important thing now is to support Italy," he said.
Prandelli did not give any interviews on Sunday when the squad was announced but had said before the decision that Rossi would be judged on his fitness and his performance against Ireland.
Fans of Rossi's club Fiorentina, a team Prandelli used to coach, were furious, but some commentators said the coach had been consistent with his previous declarations that he would not take any players who were not fully match fit.
Rossi made his Italy debut against Bulgaria in 2008 and played in the Confederations Cup the following year, scoring twice in a 3-1 win over United States.
That brought vitriolic criticism from American fans, angry that Rossi, who was born in the U.S. and lived there until he was 12, had chosen to play for the country of his parents' instead.
Rossi's unlucky run began when he just missed out on being selected for the 2010 World Cup by coach Marcello Lippi.
The following year, he suffered an anterior cruciate ligament injury while playing for Villarreal in a Spanish league match.
He fought desperately to be fit for Euro 2012, only to re-injure the knee in training the following April, causing him to miss the tournament.
He made an excellent comeback with Fiorentina this season, scoring 14 goals by early January to make him Serie A's leading scorer.
However, he then suffered a less serious injury, a second degree sprain to the medial collateral ligament, in the same knee which sidelined him until the start of this month.
Prandelli was among those who were moved by Rossi's efforts to get fit in time.
"The chance to play at the World Cup is what makes me get up in the morning," said Rossi.
Rossi, who has just recovered from his latest knee injury, took part in a week's training and played Saturday's friendly against Ireland, only to be left out when coach Cesare Prandelli trimmed his provisional 30-man squad to the final 23 on Sunday.