The four-time world champions played out a goalless draw with Sweden at the San Siro on Monday night, failing to overturn a one-goal deficit from Friday's first leg in Stockholm and missing out on a place at next summer's finals in the process.
The 39-year-old goalkeeper, who lifted the 2006 World Cup in Germany, who had been hoping to compete in a record sixth World Cup.
He said: 'There's an infinite number of things to evaluate, we'll speak with the Federation, we'll evaluate the situation'. After the match, he said: "I have not resigned because I haven't spoken to the president yet".
"It's a very heavy result to bear, because I was absolutely convinced that we had this ferocious desire to overcome the obstacle". "We couldn't do it in any other way, they are so skillful", Andersson said. Let us return to being the Italy that the entire world envied!
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Giampiero Ventura, the Italy head coach, resigned after the final whistle but only after his decisions provoked a protest from one of the Azzurri's most-experienced global players.
Midfielder De Rossi, 34, who has also called time on his worldwide career, added: 'It's a black moment for Italian football and a really dark one for us players who were a part of the past two years'.
It was a huge ask of the Brazil-born player who had not previously played a competitive game for Italy.
Buffon even came up for two corners in a final desperate gamble but Italy fell desperately short, leading to damning headlines in the Italian press.
Failure to qualify has heaped pressure on Italy boss Gian Piero Ventura, with the sport daily Corriere dello Sport calling for him to step down, while the headline in La Gazzetta dello Sport read "Italy, this is the apocalypse".
"It is an intolerable football shame, an indelible stain", the newspaper said.