Some sections of the Bianconeri's support have been extremely critical of the forward's performances but he scored a crucial goal against AC Milan on Sunday night
The 26-year-old scored within two minutes of coming on in place of Fabio Quagliarella in Sunday night's 3-2 win over AC Milan as the Bianconeri came from behind to earn three vital points.
Conte hopes that the forward's influential contribution in such a big game will finally secure him the full support of the club's followers.
"I am glad that, after being asked by people so many times about this, Giovinco finally scored a decisive goal," the Juve boss told Sky Sport Italia. "I am happy for Seba, as he gets too much criticism from the Juve fans.
"It is not fair, as he is as good as the other strikers and needs support. I hope the rapport with the supporters can improve because of this goal."
The dramatic victory against the 10 men of Milan, who had Philippe Mexes sent off, saw the back-to-back Serie A champions continue a strong start to the new campaign by making it 19 points from seven matches.
Conte says that he hasd to be impressed with such a points return but admits that his side still need to sharpen up, after conceding the opening goal for the sixth time in their last seven outings.
He continued: "When the fixture list was drawn up, everyone said we had been given a really tough start. I would have been more than happy with six wins and a draw by this stage.
"It was a good performance but we have to improve. At the moment we are conceding with the first shot on target, so that is an element of bad luck but also our own mistakes.
"We have been living with this situation for a while. It is almost as if we need a slap to wake us up. The first goal today was crazy, I almost didn't see Milan had scored after 20 seconds. After that, we did well to get back on our feet against a strong Milan side."