The 27-year-old knows that his error cost Italy an important win in Group C and says they need to stop giving their opponents chances to score
Mario Mandzukic was allowed to bring the ball down in the six-yard-box, after Ivan Strinic’s looping cross floated over the Italian's head.
Mandzukic then smashed the ball home at the back post and the 27-year-old admits he should have done better.
"I made the mistake for Croatia's goal. I gave too much space to Mandzukic. He did well to control the ball and score, but I had to be closer to him," Chiellini told reporters after the game.
It was the same story against Spain in their opening Group C game as Italy took the lead through Antonio Di Natale but were pegged back just four minutes later when Cesc Fabregas was allowed to run through and score.
The Juventus defender knows the importance of keeping a clean sheet and how tough it can be defending on an international level.
"Even against Spain we were winning and at this level it is like this. You give away a chance and they will score. In the second half we were too close to our own goal."
The two draws means Italy will have to beat the Republic of Ireland in their final game to have a chance of qualifying for the knockout rounds.