Giovanbattista Venditti scored the game's only try, with Luciano Orquera and Gonzalo Garcia kicking the Azzurri's points, as they matched their record in 2007 of finishing with two wins.
But where six years ago they beat Wales and Scotland, Parisse insists that successes over les Bleus and a first in the Championship over Ireland were proof of progress.
He said: "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.
"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."