Juve claimed their first win at Napoli’s home stadium since 2000 to move four points clear at the top of Serie A.
Paul Pogba’s stunning 29th-minute volley was cancelled out by Napoli defender Miguel Britos, but two further Juve goals from Martin Caceres and Arturo Vidal sealed the points.
De Laurentiis quickly took to Twitter to slam the officials for missing an apparent offside in the build-up to Caceres’ strike, branding them “incompetent”.
But Allegri immediately responded, criticising the Napoli supremo for “stirring up controversy”.
He told Sky Sport Italia: “It makes me smile, because if we start protesting at refereeing decisions then it’ll be chaos.
“When they go against us, everyone is happy, but when they go in our favour it’s controversy. In that case, shall we complain about the two incidents that went against us with Sampdoria [in a 1-1 draw last month]?
“Mistakes happen, they are made by coaches, players and presidents, so why not referees? Why do we want to stir up controversy after a great game?
“It’s disappointing to see someone trying to stir up trouble after such a wonderful night of football. Unfortunately this is football in Italy, as nobody accepts defeat or decisions.”
Allegri felt the result served as just revenge for their Suppercoppa Italiana loss to Napoli last month, and hailed the way his side responded to Britos’ leveller.
“Aside from that goal, tonight we played better than Napoli and fully deserved the victory,” he added. “This was like a recompense for what we lost in Doha [in the Supercoppa].
“We have many things to improve, such as the pace of the game and the speed of passing, but it was a struggle and I’m pleased we were able to win out.
“Recently we had dropped leads, but this time we fought back and reacted. In order to win we must learn to sacrifice, suffer and fight.
“Juventus won the Scudetto three years in a row, but that certainly does not mean a fourth is to be taken for granted.”