Since becoming the 'sixth' nation in 2000, Italy have repeatedly found themselves battling, often along with Scotland, to avoid the indignity of finishing bottom of the table among Europe's elite rugby union nations.
However, 2013 saw real signs of progress with the Azzurri beating both Ireland (22-15) and France (23-18).
But last year they finished with the dreaded 'wooden spoon' after losing all their Six Nations matches.
There were some encouraging signs in November, with Italy defeating Samoa 24-13 before losing narrowly to Argentina (20-18) and going down 22-6 against the Springboks.
"There's a lot of talk about the quality of our opponents, but we're a quality side too and we have top level players," Parisse said on Wednesday.
"I'm confident, because after six difficult months we showed in November that we're back to our old selves. I'm disappointed about the defeats to South Africa and Argentina, in which we lacked efficiency, but we had the right spirit. And we still have it.
"They've written us off, but that's fine. It will be great to surprise everybody," added Parisse, regarded as one of the best No 8 forwards currently in the game.
Italy welcome champions Ireland to Rome's Olympic Stadium for their Six Nations opener on February 7th, having suffered a chastening 46-7 loss in Dublin last year.
The two sides are in the same pool at this year's World Cup in England and Parisse, speaking at the Six Nations launch in London, conceded: "As Italians, we are not at the same level as Ireland.
"We beat them two years ago but last year they won by 40 points in Dublin.
"It is important for us to be competitive and see if we are really, really far from them or if we are able to play a full match at our best and beat a team like Ireland," the back-row forward added.
"It is important because we are going to play them in a few months' time at the World Cup.
"It is important for us mentally to know we can beat these teams.
"If we play 100 games against Ireland we would probably lose 98 so we have a small opportunity to beat them but we have to play every match with this ambition.
"We have to try to be competitive against every team we play at the Six Nations."
"We have shown we can be competitive and we can win like when we beat very good teams in 2013," Parisse said.
"But last year we played a poor Six Nations and that is the difference between a great team and a team who can get a great result, but do not have the same consistency.
"That is the target this year - to have more consistency, especially in the three matches we play at home."
Italy coach Jacques Brunel, in charge since 2011, said the team hadn't made the progress he would have liked.
"When I took up the post I said I'd like, in three or four years, for us to be able to say we could be challenging to win the tournament.
"Right at this moment, I'm not able to say that."
However, the Frenchman added: "In the last two training camps I've been encouraged by the team's condition, ambition and their commitment.
"In November, we worked on our defence because we had taken a step back in that department and if we manage to find the right balance and quality, we'll be a match for anybody."