However, while the Italians wasted what few chances came their way the Irish scored with both theirs through Keith Andrews in the 35th minute and then Simon Cox added a second on the stroke of full-time.
"We showed a really good mental attitude," said the 72-year-old Trapattoni. "We really wanted this win. It is just how I like to see my players perform. Italy had the majority of the possession, combined well but my players showed the necessary discipline.
"Football is not just about the 'show', it is also and maybe even more so the achievement of ones goals," added Trapattoni.
Both Trapattoni and his Italian counterpart Cesare Prandelli opted to rest several of their first choice players after they won their respective UEFA EURO 2012 qualifiers at the weekend. The Italians went on the attack from the outset in a match played in what seemed like a rather strange venue, but which is home to a large Italian community.
Cheered on by 20,000 fans, the Italians - captained by the ageing talent of Andrea Pirlo one of the few survivors from their 2006 FIFA World Cup™ triumph - came at the Irish from everywhere but only created their first serious chance in the 27th minute when Giampaolo Pazzini fired just past the far post.
Antonio Nocerino had an identical chance two minutes later, but failed to improve on his team-mate's effort. The Italians paid for their profligacy as journeyman midfielder Andrews broke the deadlock with a great effort from 20 metres ten minutes before half-time.
Italy were also hit hard by a storm that left the surface wet and greasy and impeded their more attractive and fluent passing game while they also met a wall of solid Irish defenders which proved impassable.
They were duly hit on another counter-attack right at the death when Cox slotted home to give the Irish victory.