"You want to win the first game of the championship - that is what's crucial."
Girvan Dempsey's 18th-minute try and some early attacks brought the promise of more scores but Ireland lacked a clinical edge and were almost made to pay as Italy gritted their teeth and stayed in touch.
"After the initial shadow boxing in the first 15 minutes, we had a really good patch of rugby and created several opportunities. Unfortunately, we didn't finish them off due to a lack of accuracy," admitted the Irish coach.
"Had we taken a couple of those chances it would have made our job a lot easier, but we didn't. Italy managed to slow down our ruck ball and it became very difficult to get quick ball back from the breakdown."
Ireland also suffered at the hands of referee Jonathan Kaplan. The men in green's penalty count was 18 against, and flanker Simon Easterby should have known better when he earned a 49th-minute yellow card for playing the ball on the deck after a couple of warnings.
"Our norm is to concede around six or seven penalties but we got on the wrong side of him. Therefore it was a performance which turned ugly, as it often is against Italy.
"I would have liked something more polished but that was the way it happened.
"Our missed chances kept the Italians in the game and we ended up defending for long periods of time."
Despite failing to completely recover from their World Cup woes, O'Sullivan is optimistic that his charges will improve and they will need to do so quickly with defending champions France in their way next Saturday.
"You have to believe as it goes on, you are going to step up another gear. You have to do that in France anyway and I would like to think next week we will go up another notch."