After dropping the first leg away from home 1-0 thanks to a 61st minute Jakob Johansson goal, Italy needed to win 1-0 during the second leg to send the tie into extra-time.
"It's disappointing", Buffon told Rai Sport. "We've failed something which could have been big also on a social level and this is my only disappointment".
Buffon felt that luck had not gone Italy's way, but he said that they could have no excuses. "They got the breaks and we didn't, but when things don't go your way, then you probably also have some blame too".
"Credit goes to Buffon for his sincerity through tears, his represent those of us all".
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Despite the embarrassment of a botched campaign this cycle, Buffon refused to lay the blame on manager Gian Piero Ventura. I'd like to wish these lads all the very best of luck. I want to give a hug to Chiello, Barza, Leo and Lele, who I had nearly 10 years alongside.
"I leave a squad of talent that will have their say, including Gigio Donnarumma and Mattia Perin".
"There is still a future for our football".
For Sweden, they will be making a return to the World Cup after missing out in the 2010 and 2014 editions in South Africa and Brazil respectively.
The Juventus legend insisted he was not saddened by the end of his worldwide career, which peaked with the 2006 World Cup triumph, but rather the effect the result will have on Italian football.