But Parisse says they need to make sure they end the tournament with victory in next weekend's wooden spoon clash with Scotland in Rome.
Parisse's side subsided to a fourth defeat from four games as they were comfortably seen off 24-3 by Grand Slam-chasing Wales at the Millennium Stadium.
The Azzurri's admirable rearguard action, which saw them make an astonishing 76 tackles to Wales' 14 during the first half, was not enough to derail the hosts' aspirations of a third clean sweep in eight seasons as they were barely able to fire a shot in anger on the rare occasions they enjoyed extended periods of possession.
The result means that new coach Jacques Brunel's side must beat Scotland, who have also suffered four successive defeats, to avoid ending the championship at the foot of the table for the 10th time in 13 seasons.
Having shown positive signs in Paris on the opening weekend, and narrowly missed out on a win against England in Rome, talismanic number eight Parisse says his side need to brush themselves down for one last effort to ensure there is some momentum to take forward.
He said: "Apart from the second half in Dublin it has not been a bad championship, it is our first with Jacques in charge as head coach.
"We missed the win against England by just a few points and we hope we can win against Scotland next week to end the championship on a high."
Former Perpignan coach Brunel added: "The first thing this week will be to manage the physical condition of the players as this game against Wales was very, very tough.
"Scotland are a good team and they have done well and have been very close to winning two of their games in this championship and this is a very important match for us to win."
Despite seeing his team easily seen off by a Welsh side that was someway below its best, Brunel praised the defensive effort from his players, particularly on the back of their 40-point hammering in their previous fixture against Ireland.
He said: "The spirit we have shown here was completely different than against Ireland in Dublin, especially in our defensive performance against what is a very powerful Welsh side and we kept ourselves in the game almost throughout.
"It was a weaker game from an attacking point of view especially with the line-out as we made too many mistakes there to launch any good attacks."
Scotland have been the opponent Italy have enjoyed the most success against in the championship, winning five of their meetings since 2000.
And Wales hooker Matthew Rees believes home advantage in Rome might swing the pendulum in Italy's favour.
"Italy are a good team. The one thing you will get with them is a physical edge. They never give up, and we knew it was going to be tough," he said.
"Scotland are a good team as well, but I think I would definitely go for Italy at home next week."
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