Sweden won the first leg of the match with a 1-0 victory on Friday and then secured their place in Russian Federation next summer with a 0-0 draw on Monday.
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.
'Why the f*** should I go on?
Ventura, who is under contract until 2020, apologised after the match but the 69-year-old stopped short of resigning.
De Rossi then pointed towards Insigne, who has been in excellent form for Napoli this season, to be brought on as quickly as possible. "We just had to sit there and hope that we could hang on", said Sweden coach Jan Andersson.
"It wasn't up to me whether it was a tactical issue and the Prof [Ventura] is a lovely guy, so I'm sorry if I offended anyone".
After the match a tearful Buffon, who had already made a decision to hang up his gloves after Russian Federation 2018, said 'I'm not sorry for myself but all of the Italian football movement.
The Italians, who had not missed the World Cup since the 1958 finals in Sweden, had 75% of possession, squandered numerous opportunities and had penalty appeals turned down in its increasingly desperate search for an equaliser.
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