The Nerazzurri triumphed 3-1 in Turin to close the gap on the Bianconeri to just one point.
"Inter are very strong on the counter," said Chiellini. "As soon as we lost our unity and started to leave more spaces.
"Inter took advantage and deserved the victory."
Despite the disappointment, the Italy international said that there is still a lot of football left between now and the end of the season.
"We are still top of the table and in the Champions League, so we have a lot to give."
Juve will look to bounce back when they travel to Pescara next Saturday.