Allegri's opposite number Zdenek Zeman abandoned his preferred 4-3-3 approach in favour of a four-man midfield, but it did not have the desired impact as Carlos Tevez pounced from close range before a sublime strike by Arturo Vidal gave Juventus a 2-0 lead with a quarter of an hour played.
By the time Luca Rossettini pulled a goal back for the third-bottom hosts, Fernando Llorente had netted early in the second half as Zeman's plans received a further blow.
"I was astonished by the change of system and did not expect it," Allegri told Sky Italia.
"Considering the difficult moment they are going through and the fact they were up against Juventus, Zeman tried to close up the spaces and go on the counter. We did well to avoid running into difficulties."
The win guaranteed top spot for Juventus heading into the mid-season break.
Allegri and his players now turn their attentions towards Monday's Supercoppa Italiana against Napoli in Qatar.
"It was important to end 2014 on top of the table so that we can prepare at our best for the Super Cup," he said.
"We will play to the max without thinking about Inter [Juventus' first game back] after the Christmas break.
"I am fortunate to train a group of players that wants to win and continue amazing people.
"I have a lot of faith that this side can do well in Europe too."
Nevertheless, Allegri was critical of his team for allowing Cagliari a route back into Thursday's match when the points appeared to be sealed.
He added: "I was angry towards the end because in modern football a game isn't over until it's over, especially against a Cagliari side that never gives up, so we should've controlled the situation better when 2-0 and 3-0 up.
"After their goal we started playing again, but we shouldn't run risks like that."
