The Bianconeri scraped a derby win on Saturday night, and Giovinco admitted his team could have performed better overall.
Many first-team players were rested ahead of the decisive Champions League clash against Chelsea, and that might explain the Bianconeri's slow start against the Granata.
"It was a good game, even though we did not start too well, but then we managed to recover," explained the former Empoli player to Sky.
"Obviously, we can do better. I'm happy about my performance. It was an important game, as the derby is a different match which is felt a lot by the fans, so we really wanted to win."
In the end, the match was decided in the final ten minutes by a goal from defender Giorgio Chiellini, keeping Juventus within seven points of Inter in the title race.