The Turin giant had needed just a point to officially seal its 34th Scudetto and become the first team to complete the league and Cup double for four consecutive seasons.
Meanwhile, Maurizio Sarri's Napoli won 2-0 in Sampdoria to give them the meagre consolation of a new club record of 88 points.
With one match left to play Juve can not be caught by second-placed SSC Napoli, who are four points behind after winning 2-0 at UC Sampdoria. "It's hard to see these four years being repeated", Allegri said. "Credit goes to the lads for keeping their cool, taking things one step at a time towards our final objective".
"If you get overwhelmed by enthusiasm, you're going to collapse three days later".
Third-placed Roma, who had already secured a place in next season's UEFA Champions League, have 74 points.
"Behind their successes there is a mentality which has been built over the years", Roma coach Eusebio Di Francesco said.More news: Float in Disney's Festival of Fantasy Parade catches fire
"I'm in charge of a fantastic squad made up of some great players, backed by a club which has always supported us, even in moments of difficulty. They are an example for other teams to follow".
Juventus had early chances with Edin Dzeko firing over, a Lorenzo Pellegrini right footer flying wide and Aleksandar Kolarov's free-kick hitting the side netting.
Paulo Dybala had a goal disallowed for the visitors but they rarely threatened Alisson in the hosts' goal.
But Juventus did not take advantage of their advantage as they game lost its momentum although Dybala did have penalty appeals.
"It's not an issue of decisions on the future; it's about planning what the future of Juventus will be because once we've finished celebrating, we have to sit around a table with clear heads".
Chiellini is one of five players who have been involved in all seven title-winning campaigns alongside goalkeeper Gianluigi Buffon, defenders Stephan Lichtsteiner and Andrea Barzagli and midfielder Claudio Marchisio.