Ireland were left to rue a 15 torrid first-half minutes that saw Luke Marshall, Keith Earls and replacement Luke Fitzgerald all go off injured, flanker Peter O'Mahony end up on the wing and Brian O'Driscoll sent to the sin bin.
After the break Italy captain Sergio Parisse was also shown a yellow card and while he was off the pitch, Ireland enjoyed their best passage of play, moving to within just a point behind at 16-15 with 17 minutes remaining.
But two more penalties from Orquera inflicted defeat on Ireland, who have now lost three and drawn one of their last four matches after an opening victory over Wales.
Injuries have been a key feature of all Ireland's campaign while they will be left to rue missed opportunities in all of their last four matches - most notably in defeat to Scotland at Murrayfield.
But Heaslip believes Ireland will be all the stronger for their disappointment.
"This young squad will have learned a lot from this," he said. "Guys have stepped up and taken their opportunity and will have learned a lot going forward.
"This kind of experience will be good for this kind of squad. But it's been a frustrating one, with games that had only one or two scores in them.
"Things just didn't go our way and we just have to learn from this.
"We gave away too many easy shots at goal and also turned over a lot of ball at the set-piece. They cut us off at source.
"The set-piece is a big launching platform for any team, so to lose that was frustrating. But we were still in it until the end, despite the injuries."