The interim boss has highlighted the importance of the midfield duo for not shirking responsibility during the opening-day victory, and spoke of his role in Antonio Conte's absence
Second-half strikes from Stephan Lichtsteiner and Andrea Pirlo were enough to ensure the Old Lady started the defence of their Scudetto shield in winning fashion, despite a slow start in Turin.
However, Carrera, who has assumed caretaker responsibilities on matchdays following Antonio Conte's suspension, believes the victory must be attributed to a rise in performance levels of the two midfielders.
"Vidal felt that he was being pulled by one of the Parma players [in the build-up to his missed penalty]," the former Italy defender told Sky Sport Italia.
"During the first half, we maintained a slow pace, then Marchisio and Vidal grew and the team followed them."
Carrera then reflected on the displays given by summer signing Kwadwo Asamoah, who has impressed in an unfamilar left-wing position since his arrival from Udinese, and makeshift centre-back Luca Marrone.
"We tested Asamoah in that role during pre-season and he has shown that he can offer a lot there. His play was spot on," he added.
"Marrone in defence? He is doing well, but he has to work hard; he needs a little more experience."
The ex-Juve and Atalanta stopper has enjoyed a successful start to his spell in charge of the Bianconeri, having also won a Supercoppa title prior to the weekend, but he insists he is not thinking about the possibility of replacing Conte permanently.
"Antonio is a great coach with great charisma. I aim to bring the charge that he gives us on training onto the pitch," mused Carrera.
"In the match, I make the decisions. We work together and know each other's methods.
"Do I want to be the head coach? No, we want to continue with Conte."
Juventus temporarily sit top of Serie A following their win, having bettered Fiorentina's 2-1 victory over the Zebrette earlier on Saturday.