Alessio oversaw the win for the reigning champions that saw them return to the top of the Serie A table.
The Italian insisted that the game was always under their control, despite a fightback from a spirited Chievo side.
"The game was always in our hands," said Alessio. "In the first half we scored two goals and could've had more. We only failed to control the match properly in the opening 10 minutes of the second half.
"It is becoming a recurring theme that we concede on our opponents' first shot on goal, but we were in control and it was important to earn the three points today.
"We didn't lose our cool. We are relaxed and have always played to the best of our abilities. Now we continue along our path, knowing it is more difficult than last season."
Juventus face Fiorentina in Serie A next Sunday.