Since five nations became six, Italy have finished fourth just once - in 2007 - while in the autumn they defeated Tonga, lost to New Zealand and also went down to Australia, although they pushed the Wallabies close in a 19-22 defeat.
But 29-year-old Parisse, who has 91 caps to his name, is adamant that Italy must begin the RBS 6 Nations on the offensive.
"It's no longer enough for us to play well, to be improving and be involved in good matches," said Parisse, speaking at the official launch of the RBS 6 Nations 2013 in London.
"The gap between us and the other teams is closing, but for the credibility of the team we need results.
"We've been improving since we've been in the Six Nations and this year because we have three games we hope to do well.
"We don't have fear of any team in the Six Nations and we want to confirm our progression by winning matches."