Published Monday, 18 June 2012
Mario Balotelli of Italy scores his side's second goal against the Republic (© Getty)
Giovanni Trapattoni's side was led by winger Damien Duff on his 100th appearance for his country and wore black armbands to mark the 18th anniversary of the Loughinisland massacre.
The side will return to Dublin on Tuesday having failed to collect a single point in the tournament.
Their exit from the competition was confirmed last week after a heavy defeat to Spain, but Ireland showed more resistance on Monday night conceding one goal in each half, which fired Italy into the quarter-finals of the championship.
Italy needed a win to go through in second place as reigning champions Spain topped Group C with a 1-0 victory over Croatia in Gdansk.
Antonio Cassano first headed home from Andrea Pirlo's 35th-minute corner before substitute Mario Balotelli added a second goal at the death.
The Republic staged a late assault on the Italian goal which came up only just short.
Gianluigi Buffon had to be at his best to keep out Andrews' drilled 79th-minute shot from Duff's back-heeled free-kick.
But it turned sour as Andrews, who had earlier been booked for a foul, received a second yellow card for dissent at the end of the game, seconds before Balotelli fired home a Pirlo corner to secure the win.
We're all disappointed, but we've been beaten by better teams.
After the match striker Robbie Keane said the Republic of Ireland had come up short of the required quality on the Euro 2012 stage.
Keane also paid a heartfelt to the Irish fans, who have been dubbed the best supporters in the world during the tournament.
"The last three games, they've been fantastic," he said.
"It's a shame we didn't perform as well as we can and perform for them because if anyone deserves it, it's them.
"I think we played well tonight without really creating too many chances. It's one of those things. It's certainly disappointing we didn't get something out of the group."
Keane said the side, who enjoyed a 14-match unbeaten run before the start of the competition, had conceded too many soft goals through poor defending.
"It's set-pieces again and it's been the same in the last few games. It's one of those things because in previous games we've been quite solid in that department."
Asked if this was likely to have been the final appearance for several veteran players, the 31-year-old Los Angeles Galaxy forward said: "We'll have to see."
This was the Republic's first major tournament for a decade and their first Euro finals since 1988.