The Italians failed to repeat their victory over Wales on the opening weekend of the 2003 RBS 6 Nations but despite his disappointment, Kirwan was full of praise for the impressive Irish.
"The Irish have to be happy with their game," he said. "Their Six Nations is on track."
The Italians, who lost record points-scorer Diego Dominguez with a knee injury early in the second half, caused plenty of problems early on for the visitors and at least they managed to breach the Ireland defence for the first time in the championship.
"We probably needed to take a few more risks," admitted Kirwan. "Ireland shut us down in the line-outs and we lacked patience. We needed to have the confidence to hang onto the ball and work our phases.
"We should have taken our chances. We nearly scored three times and we needed to put them away."