Italy's Mario Balotelli posted a short clip on Instagram before the game, sending a message to the fans wishing his country good luck.
Ibrahimovic, 36, retired from worldwide football after Euro 2016 and coach Janne Andersson was annoyed to be asked about whether the striker might return for the finals in Russian Federation immediately after the play-off win.
"I'm not sorry for myself but all of Italian football, because we failed at something which also means something on a social level".
Italy won the World Cup in 1934, '38, '82 and 2006, and had qualified for every tournament since 1958.
Buffon was seen applauding the Sweden anthem as Italy fans booed at the San Siro. "We just had to sit there and hope we could hang on".
What is the World Cup without Italy?
The former Torino coach has been under pressure ever since Italy failed to top their qualification group, and their World Cup failure is seemingly the final straw. "Not taking part in the Russia World Cup is an enormous slap in the face". I regret just that my final match with the national side coincides with an elimination.
10 defeated Italy 1-0 at their home court in the first leg of the playoff draw.
Ventura, 69, is under contract until 2020. Play-offs are decided by episodes and they went against us but you can understand that when you're at fault.
Ventura had made changes from Friday's defeat with Brazil-born Jorginho making his Italy debut and Alessandro Florenzi and Manolo Gabbiadini also handed starts, although Napoli's in-form winger Lorenzo Insigne was again left on the bench.
"Wasted chances, a bit of bad luck but zero goals in 180 minutes against the Swedes, who will go to Russia", Gazzetta commented.
"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.