It was the Azzurri's first victory in the fixture since joining the tournament in 2000 and combined with their triumph over France, it completed their greatest overall championship performance.
They also registered two wins in 2007 - against Scotland and Wales - but Parisse insisted the quality of opposition they have mastered this year sets 2013 apart.
"You can't compare this Six Nations with 2007 because we have secured wins against two squads with a lot of history, two of the strongest in the world," the Italy captain said.
"We're a squad that's improving. We play France and Ireland in the group stage of the 2015 World Cup and we have sent a strong message to them.
"There were a lot of positives in this game from a psychological point of view because there was a good balance between our backs and forwards.
"In this Six Nations we have managed to put a lot of teams under pressure. We played against some great players like Brian O'Driscoll, but have nothing to be envious of."
Wing Giovambattista Venditti burrowed over for the game's only try in the 49th minute, but Italy could have finished with several more and were grateful that Luciano Orquera and Gonzalo Garcia had brought their kicking boots.
"With this victory we showed we were capable of producing some continuity," coach Jacques Brunel said.
"We've shown a good level to our game in this Six Nations. We are a work in progress, but we have shown character and spirit.
"At times there was a lot of composure to our game and that shows we are on the right track."