Manolo Gabbiadini played his part but could not help Italy progress through to the World Cup finals at the San Siro.
Trailing from the first leg 1-0, Italy were on the front foot as they pursued a response to Jakob Johansson’s solitary strike in Stockholm.
The Azzurri’s first major chance fell to Antonio Candreva, who collected a pass inside the box before firing a rising, right-footed shot over the bar.
With Saints forward Gabbiadini impressing with his link-up play and intelligent movement inside the San Siro, Italy continued to press and had another chance through Ciro Immobile shortly before half-time.
Jorginho’s incisive through ball found the Lazio forward, who saw his effort saved by Robin Olsen before Andreas Granqvist cleared off the line.
On 63 minutes, Gian Ventura made a double change with Gabbiadini being withdrawn for Andrea Belotti but a goal eluded them meaning its the first time they have failed to qualify since 1958.