Sportal.co.nz 17.Nov.2012Getty Images
The last time the two countries clashed, the All Blacks laboured to a 20-6 win in Milan three years ago, and Parisse said his team are playing better rugby now.
"I think that the team has showed some improvement. In 2009, the result achieved in Milan was quite impressive," he said.
"I know that it's always difficult to see a defeat as a positive result, but we've got to put this into perspective and say that the All Blacks are much stronger than us.
"Despite this, they really struggled against us in 2009 - they only scored one try and I think we'd have deserved to score one too after all those scrums.
"Since 2009 anyway I think that we've really improved, at least this is my perception from within the squad. I feel we are stronger. But I'm also aware that we're constantly under the spotlight."
Italy defeated Tonga 28-23 last weekend, and Parisse feels his side can enter the match in Rome without the burden of expectation.
"We don't feel any pressure anyway because nobody expects a win from us tomorrow, but we do expect to perform and improve in respect to last week's [game]," he said.
"We feel more relaxed. The same fact that we won't feel the pressure of the result remains important.
"In the past, sometimes we struggled to cope with the pressure and we made mistakes that we normally wouldn't make because we had to win.
"Apart from this, I firmly believe that we'll have to show our improvement. It's not the result that matters against New Zealand, but our performance during the full 80 minutes."