It did so on the back of two qualifying campaigns which suggested it was capable of doing just that, and having earned the respect of even the biggest teams on the continent in the process.
In the event, its stay in
However, a nation raised on the heroics of the 1988 European Championships - the last for which it qualified - and the World Cup finals of 1990, 1994 and 2002 expected much, much more, and the ensuing bout of introspection has left Trapattoni and his employers with serious questions to answer.
The 73-year-old Italian presented a defiant front as he surveyed the wreckage of a campaign which disappointed and surprised in equal measure, and he swiftly turned his attention to the qualifying campaign for the 2014 World Cup in
Trapattoni said: "In my life I have had many successes and been the manager of great teams.
"I have always had the habit of winning and not losing and when I lose, I don't sleep at night. I think about if I have made mistakes.
"The willingness is there to come back with fresh energy and a new squad to do better, and I can't wait for the new season to start."
Trapattoni insisted he was going nowhere amid suggestions in certain quarters that the time may have come to part company with a man whose approach to the game has always had its detractors.
But the nature of
Under Trapattoni, the Republic has risen steadily in FIFA's ranking list - it arrived in
Along the way, Trapattoni's reliance on a 4-4-2 system with two holding midfielders attracted criticism for its rigidity and conservatism, but the manager more often than not was able to point to results as the only justification he needed.
However, he was unable to offer that as a defence in
The Croatians ran out 3-1 winners in Poznan and a shell-shocked
It rallied against
Trapattoni's perceived inflexibility was a main thrust of the arguments against, but while the veteran Italian undoubtedly made mistakes, he was not alone.
Dunne admitted: "As much as we wanted to do well, we know we haven't. We are playing against teams that are better than us and it's hard to accept that our best at the moment isn't good enough."
Trapattoni has already indicated that the likes of
But just how far he himself is prepared to adapt remains to be seen.
UEFA president Michel Platini said preparations for Euro 2016 were "progressing well" after a meeting of the organising committee in Lille.