France head coach Fabien Galthié said he had been left with a "bitter taste" after his team opened their Guinness Six Nations defence with a nervy victory over Italy in Rome.
Having been 19-6 up midway through the first half, France then found themselves behind in the second before Matthieu Jalibert's try saw them claim a 29-24 win.
Galthié, whose side will now face world No 1-ranked Ireland in Dublin next Saturday, told L’Equipe: "We are satisfied to have won it, to have taken the offensive bonus – two of the objectives we had set ourselves – but we must admit that it was hard.
"The performance is mixed to say the least, it leaves us with a bitter taste. We didn’t achieve all our goals in this game, that’s clear.
"But we have the right, collectively, not to always be on top, always be in line with our expectations that have evolved over the past two years.
"We must say that winning an international match, in the tournament, away, is already important. Now we are aware that we must do much better."
France conceded 18 penalties and defence coach Shaun Edwards said major improvement is required ahead of their trip to the Aviva Stadium.
Edwards told ITV Sport: "First half, we were quite dominant. They came on leaps and bounds in the second half and obviously at the end it was a very tight affair, but we are in a good habit of winning tight games at the moment.
"It happened against Australia, against South Africa, it's happened in a few games.
"Hopefully we can continue that habit, but I think we all know if we don't put up a better performance next week we'll be on the end of a 15-30 point hiding."
As well as Jalibert, Thibault Flament, Thomas Ramos and debutant Ethan Dumortier got on the scoresheet for France, while Ange Capuozzo dotted down for Italy, who also were awarded a penalty try, and Tommaso Allan added four penalties.
Italy head coach Kieran Cowley told a press conference: "I am really satisfied with the character and conviction with which we approached the match.
"In the first half there were some problems of execution, mistakes that must be avoided and that cost us a lot.
"For the rest our scrum was fantastic, despite the considerable difference in weight in the front line, in defence we did very well, and the way we came back in the second half is for me another reason for great satisfaction, how we were able to modify our game adapting to the mood of the match showed great maturity.
"Unfortunately, the defeat is the result of those [mistakes] seen in the first quarter, at these levels concessions cannot be made and against England [next Sunday at Twickenham] we will absolutely have to avoid them."