Italy captain Sergio Parisse said his side deserved their stunning 23-18 victory over France in their opening fixture of the Six Nations.
Italy went down to 14 men in the last two minutes when Davide Giazzon was sin-binned but resisted France's attempts at a push-over try.
"If they'd scored in the last minute we would have been really disappointed - we deserved that victory," he said.
Prop Martin Castrogiovanni said Italy would "have a chance against any team".
"We can't start the tournament better than this," the 31-year-old tight-head told BBC Sport, with a trip to Scotland's home Murrayfield awaiting the Azzurri next week.
"We repeated what we did two years ago. We still have another four games and I hope we can play like that again. If we do, we have a chance against any team."
Home skipper Parisse went over in the first five minutes to give the Azzurri an early lead before France fought back.
But a Martin Castrogiovanni try, 10 points off the boot of Luciano Orquera and good defending secured the win.
"I'm happy to score, but it was good day for the whole team," said the Stade Francais number eight. "We defended really well."
The visitors, perennially among the pre-tournament favourites, took a 15-13 lead into the interval thanks to tries from Louis Picamoles and Benjamin Fall, and Frederic Michalak's penalty extended their advantage soon after the restart.
But a brilliant offload from Orquera allowed Leicester's Castrogiovanni to dart over, before replacement Kristopher Burton added a great drop-goal to give the Italians some breathing space.
Despite a late French onslaught, the the home side held on for a repeat of the shock success over Les Bleus in 2011.
France coach Philippe Saint-Andre said his side made "too many mistakes".
"I want to congratulate Italy - they played with a lot of passion," Saint-Andre told BBC Sport. "We had opportunities to score, but we lost too many balls."
"We have to be very focused in order to play well against Wales at the Stade de France next week. [We] are very, very disappointed. We prepared well. We need to realise that the Italians are improving year by year. They were unlucky to lose to Australia.
"We had control, but we made too many mistakes. We respect Wales, but we need to win. It's not acceptable to lose at home."
Italy's former captain Marco Bortolami said he did not think the French were in the right frame of mind.
"We [Italy] struggled with discipline towards the end, but what a win," he told BBC Sport.
"Their body language was a disaster. They were here, but didn't know how to win this game. It was a big game for Italy. Next week, we travel to Scotland, so who knows?"