Juventus are five points clear at the top of the Serie A table with seven games remaining and on track to claim their third consecutive Scudetto crown.
There were joyous celebrations as Napoli, third in the standings, ended Juve's 22-match unbeaten streak courtesy of a shock 2-0 victory last weekend.
However, Chiellini took Napoli's celebrations as a compliment to his club's overwhelming success since their promotion from Serie B in 2007.
"I don't think it was excessive, it was just the simple celebration of those who want to win and not finish second," said the 29-year-old.
"Is it Juve against the rest of Italy? It's been like that since the start of the season.
"When Juventus lose, everyone celebrates because they hope the title race will be open again. The more you win, the less people like you.
"Of course, I hope next year they'll like us even less..."
Last weekend's loss opened the door, albeit slightly, for second-placed Roma, who have played one game more than Antonio Conte's men.
Juventus have the chance to bounce back when they host third-bottom Livorno on Monday and Chiellini knows victory at Juventus Stadium would dent the hopes of Roma.
"We have the Scudetto in our grasp, but that doesn't mean we've already won it," said Chiellini.
"Now we need to bring it home. The fixture list might appear simple on paper, but there are dangers, starting from Livorno.
"On the other hand, Roma can play without pressure. They've had an amazing campaign, beyond their rosiest expectations."
