Italy's Mario Balotelli posted a short clip on Instagram before the game, sending a message to the fans wishing his country good luck.
After the game, midfielder Daniele De Rossi and defenders Giorgio Chiellini and Andrea Barzagli announced they would be retiring from worldwide competition - joining goalkeeper Gianluigi Buffon, who previously said he would do so after the World Cup.
Italy have played in the last 14 World Cup finals, winning two of them.
Sweden survived wave after wave of Italian attacks in the second leg of their European playoff on a night of unremitting tension and drama at a disbelieving San Siro.
The defeat heralds the end of the global career of goalkeeper Gianluigi Buffon, the most capped player in Italian history with 175 appearances for his country.
Reports in Italy claimed Italy manager Gian Piero Ventura had resigned following the 1-0 aggregate defeat.
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Ibra is Marmite, but his imagination with the ball and raw presence deserves a final shot at the World Cup.
It was also the tear-jerking end to the career of their 39-year-old goalkeeper and captain Gianluigi Buffon who made his Italy debut 20 years ago against Russian Federation - on the last occasion that Italy had to face a playoff for a World Cup place. "A World Cup without Italia is like pizza without cheese".
Ventura, 69, is under contract until 2020.
"It is really very sad because watching the World Cup was something that really brought us together as Italians", said recent graduate Stefania Pusateri, heading for the exit after watching the match in a Rome bar.
The embattled Ventura faced criticism during Italy's game from one of his own players, with veteran midfielder Daniele De Rossi left aghast when he was asked to warm up. "We just had to sit there and hope we could hang on. At the time I just thought perhaps it was better that Insigne come on instead".
"Apocalypse Azzurra", said the headline of La Stampa newspaper, referring to the unofficial name of the team whose bright blue jerseys reflect the azure of the Mediterranean Sea.
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