Strikers Carlos Tevez, Fernando Llorente and Alvaro Morata all grabbed doubles in the victory at Juventus Stadium, with Stephan Lichtsteiner also getting his name on the scoresheet.
Having waited 23 minutes for the opening goal, Juve kept punishing Parma at regular intervals to record their biggest league win since 1983.
Allegri was quick to praise his side's efforts in front of goal, after putting more emphasis on their finishing in training after wasting chances in recent performances
"Training's there for a reason," said the head coach. "And if we get used to hitting the target during the week, we'll do so on matchdays as well.
"We've got an excellent group of strikers, from the ‘older’ players like Tevez and Llorente, to the younger ones like [Kingsley] Coman and Morata.
"We had a couple of issues in the first 15 minutes, but then we broke the deadlock and the lads read the game well. I'm very happy."
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