Italy win 4-2 on penalties
And, as on five of the previous six occasions England have entered this sudden-death environment, they were left heartbroken, with Italy confirming a semi-final meeting with Germany in Warsaw on Thursday.
England captain Steven Gerrard and Wayne Rooney were successful from the spot, but Ashley Young struck the bar and Ashley Cole's effort was saved by Italy keeper Gianluigi Buffon.
Mario Balotelli scored Italy's first spot-kick but Riccardo Montolivo's miss gave England hope that was cruelly snatched away as Andrea Pirlo audaciously chipped in his spot-kick and Antonio Nocerino coolly slotted home before former West Ham midfielder Alessandro Diamanti scored the decisive penalty.England cannot complain that the better team did not emerge as winners - but even in the face of a constant wave of Italian attacks Hodgson's men still showed enough heart and durability to make their Euro 2012 exit with pride.
As Italy subjected them to what was almost torture by possession, England's back four and goalkeeper Joe Hart responded magnificently by erecting a wall of defiance, with John Terry outstanding.
England will head for home on Monday after a campaign they can reflect on with a measure of satisfaction despite the disappointment. Hodgson - at short notice - marshalled his forces effectively but the gulf in class with Italy was clear and his team looked jaded long before the end.
Hodgson will now take stock of events in Ukraine, where England drew with France and won against Sweden and Ukraine to top Group D, as he plots the qualifying campaign for the 2014 World Cup in Brazil.