Mario Mandzukic, Paulo Dybala and Gonzalo Higuain all got on the scoresheet as the champions began their latest title defence in emphatic fashion.
It might have been different had Buffon not palmed away Diego Farias' spot-kick, the first penalty awarded by the video assistant referee (VAR) in Serie A history following a foul by Alex Sandro.
Allegri conceded the new system will take a period of adjustment but is relieved he can still call on his 39-year-old skipper to deal with any scenario.
"We'll have to get used to waiting for the decision," Allegri said of VAR after the match.
"In this case it was a penalty against us but fortunately we have the best guy around in goal – he sorts out all sorts of problems for us.
"We defended well out there, especially after the penalty. Before then we let them in a few times, including the move that led to the penalty itself.
"All things considered we performed well at both ends of the pitch."
Their task will be made easier if star attacker Dybala, who has inherited the Bianconeri's famous No.10 shirt, can repeat his goalscoring feats of the past two seasons.
"It's not easy to follow in the footsteps of so many fantastic players who have worn the shirt before me and I'm not going to carried away after today," the 23-year-old said.
"I need to keep going as I am."
Juve's next assignment is a trip to Genoa, who finished 16th last season.