A brace from Arturo Vidal and a late Stephan Lichtsteiner goal secured a 3-0 victory over Cesena in Turin, but Allegri, who replaced Antonio Conte in the summer, was quick to suggest that there was more to come from the defending champions.
"Every coach trains the way he thinks is best and has different ways of expressing his ideas," the Italian told reporters. "Conte's Juventus had three years of excellent results.
"I am fortunate to be Juventus coach. I think each game lasts 90 minutes and you have to read it.
"I inherited a side with great organisation, but this team still needs to improve a great deal."
Juventus meet Atalanta on Saturday night.