Les Bleus, who lost on their last visit to Rome, looked on course when they led 18-13 in the second half, before slumping to a 23-18 RBS 6 Nations defeat.
After conceding an early try to Sergio Parisse, France began to find their groove, and tries from Louis Picamoles and Benjamin Fall gave them a narrow half-time lead.
A Frederic Michalak penalty early in the second half stretched the lead to five, and when Maxime Machenaud cut through they looked set to extend that advantage.
Instead Italy turned the ball over and went the length of the field to score through Martin Castrogiovanni, and from there, France appeared to crumble.
And Saint-André, who had led his side to three victories in as many games in the autumn, admitted his team had let the initiative slip away from them in the second half.
“Italy played very well, with a lot of passion, they kept the ball well. But after we had control of the game in the second half, we were five points in front, we had the chance to score but we lost too many balls,” he said.
“We conceded two tries on turnovers and were not precise enough. When you aren’t precise enough in the Six Nations you are punished.
“So congratulations to the Italian team and we need to be very focused to play well on Saturday in the Stade de France.
“The players are very disappointed because we prepared the game well, we respected the Italian team. We need to realise the Italian team has improved each year, in November they did very well.
“They were unlucky against Australia. All the nations will come here and find it tough. What is frustrating is when you have control and have the opportunity to win. But we made too many mistakes.”
French Grand Slam hopes are now over but they will have the chance to bounce straight back when they face Wales in Paris next Saturday.
And after only their third-ever loss to the Azzurri, Saint-André warned that les Bleus cannot afford to slip up on home soil.
“There have been three fantastic international games, very quick and very physical,” he added.
“We must be focused, we play at home against Wales in the Stade de France and we need to show a better image than we did today. We need to win, it’s not acceptable to lose at home in the Stade de France.”
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