Graziano Pellè was able to equalise temporarily, but Les Bleus ran out the winners on Giampiero Ventura's debut in Bari.
“I am well aware I could've done better. It was not an easy game, we tried to play and on Monday must certainly be more focused," Chiellini told Rai Sport.
“On Olivier Giroud's goal the ball was low, I didn't have time to turn and see him. I should've read the situation better beforehand. I think all of us could've done better on the goals."
This was Ventura's first game in charge, though he only spent three days with the squad.
“Every Coach has his own style. Ventura made a good impression on the group and we hope to continue building, as we mustn't throw away what we built over the last two years, especially the last 50 days together," continued the Juventus defender.
“We need to speed up the way we move the ball around and are working on certain tactical adjustments. I don't think it'll take much to make the step up for the next game.
“The away games are very, very, very important and the trip to Israel must be faced with solidity and hard work. It'll be very important to emerge with a victory."