The Azzurri claimed a well-deserved 30-22 triumph over Steve Hansen's side at the Stadio Flaminio, and Kirwan said: "The players produced the game of their lives.
"(This) was all about finding our sprit and passion. We have talked all week about getting a passion for the game and finding our style and that's what we did.
"It shows we are going in the right direction but it is important we keep calm about it all. But we are a very happy side at the moment.
"We wanted a win and it was a very important one for Italian rugby. Now we have got that we have got to keep working.
"We'll enjoy the night but I will be watching the video and getting back to work and looking towards Ireland next week.
"We have been putting a lot of effort on our fitness for the past six months and that showed. In the last 10 minutes I did not have to make any changes."