The Serie A leaders went into the game hoping to extend their 49-match unbeaten streak in the league, but were beaten after a Diego Milito double and Rodrigo Palacio strike cancelled out Arturo Vidal's first minute opener.
"In all honesty, I expected them to man-mark Andrea Pirlo, but wasn’t sure if it’d be Fredy Guarin or Palacio," Chiellini told reporters.
"That’s how they approached Fiorentina with Coutinho coming back, but this time they seemed to alternate.
“Inter are very strong on the counter and until we kept our balance to lock down those spaces, we were in control and had the chances to add a second goal.
“As soon as we lost our unity and started to leave more spaces, Inter took advantage and deserved the victory.”
And though disappointed to taste defeat in the league for the first time since the 2010/11 season, Chiellini remains confident of continuing what has been a strong start to the season.
“Tomorrow we’ll analyse the game and try to work out the mistakes we made to ensure they don’t happen again," he stated.
“We are still top of the table and in the Champions League, so we have a lot to give.”
The Old Lady are now just a single point ahead of the Nerazzurri at the top of the table and will take on FC Nordsjaelland in the Champions League on Wednesday.