Italy, just like Sweden, ends up in the playoffs at the end of March.
Italy, European champions as late as last summer, barely created anything in the second half.
In the end, Northern Ireland came close to winning when goalkeeper Gianluigi Donnarumma made a headless fumble.
Conor Washington, who had rounded Donnarumma, however, failed to score.
The ball was stopped at the last minute by the Italian captain Leonardo Bonucci.
At the same time as Italy's national team captain Roberto Mancini went out with his head down, there was a party in Lucerne when Remo Feuler celebrated the 4-0 goal in front of dedicated fans in a large flag sea.
After eight minutes of extra time, a big hug party broke out on the pitch and in the stands.
There were some tears of Swiss happiness.