The 25-0 defeat to the French was the Azzurri's second loss of this season's RBS 6 Nations following their 50-9 home reverse to England in their opening match.
But having now played the two favourites, Kirwan believes Italy can still achieve their tournament objective of winning at least one game.
"The most positive thing about our team was their courage and we hope we are going to win a match by the end of the tournament," Kirwan said.
Next up for Italy is a home game against Scotland and Kirwan has targeted that match as a chance for them to earn only their third ever win in the competition.
"We have to improve our throw-ins and our ball retention, (but Scotland) are at our hands, we know we have the means to beat them," he said.
Although Italy were virtually anonymous in attack against the French, Kirwan was delighted with their performance in defence.
Playing with passion and tenacity, Italy limited France to just a 10-0 lead at the break and that was only courtesy of a superb try from number eight Imanol Harinordoquy.
Harinordoquy produced another impressive finish to add another try midway through the second half before replacement Pepito Elhorga raced half the length of the pitch to add a third late on against the tiring Italians.
It was certainly a better performance than against England where Italy, after a good start, conceded seven tries to the world champions.
"We improved our defence a lot, it was solid all through the middle of the match, but a couple of individual actions from France cost us tries.
"But as whole it was pretty outstanding defence from our team," said Kirwan who admitted they now needed to work on other parts of their game ahead of the Scotland match.
"We tried three or four combinations in attack but we lacked success, we are going to work on our attack in the next week.
"I am optimistic for the future, we keep improving."