The game at the Stadio Artemio Franchi ended 1-1, with Arkadiusz Milik opening the scores for the visitors while Ivorian Cristian Kouame levelled matters for the hosts.
Juventus were indebted to goalkeeper Mattia Perin, who prevented his side from going behind when he saved Luka Jovic's penalty on the cusp of halftime.
But Allegri was not impressed with the manner Juventus conceded the equaliser, which left them with just two wins in their opening five games, although they are yet to taste defeat.
"Getting angry is an understatement, you should not concede that goal. At that moment we had to kill the game," Allegri said after the game.
Allegri added: "In the second half we dropped [back], but the thing to improve absolutely is that when you have the ball when leading.
"From that ball [from McKennie] then came the corner [for Juve] and the 1-1, which changes everything."
Allegri opted to leave top scorer Dusan Vlahovic on the bench but defended that decision as Juventus begin their Champions League campaign at Paris Saint Germain on Tuesday.
The former AC Milan boss added: He said: "He had played several games and Milik could give us an extra hand. We wanted him to rest, then there were some forced changes."
