Giovinco put in an eye-catching performance and had a hand in both goals as the Serie A champions swept aside their opponents to set up a last 16 UEFA Europa League clash with Fiorentina - the only team to defeat them in the league this season.
Giovinco combined with fellow forward Pablo Osvaldo after 18 minutes and although his shot was saved, Arturo Vidal lashed home the rebound.
Juve's front two combined splendidly again 12 minutes before half-time as Giovinco put a cross on a plate for Osvaldo to head home from close range, and Conte believes the 27-year-old's performance was the perfect response to any critics.
He told Sky Sport Italia: "In order to continue in Serie A and the Europa League I need everyone. Some of these lads are mistreated by the critics, but they can gain confidence and form by playing well in these games.
"Giovinco did well with the assists, but he is right to get angry when he doesn't score. He is a striker, so he should want to score goals."
The Juve boss was happy with the ruthless approach of his side who would have scored more in the first half were it not for the heroics of Onur Kivrak in the Trabzonspor goal.
"I did say yesterday that people shouldn't expect us to come here and defend. We tried to score from the start and that's what we did," Conte said.
"I am very happy, as it is certainly a better performance in every way compared to the first leg.
"We approached it the right way, whereas in Turin we only did what we wanted to in fits and starts."
This year's final is being held at Juve's stadium but before they can begin to think about that, Conte's side face a 'very difficult obstacle' in Fiorentina in the next round.
He said: "Inevitably when two teams from the same country meet at the round of 16 it is never good, as we want all the Italian clubs to go as far as possible in the competitions.
"We picked Fiorentina in the draw, we face them with a strong desire to go forward and realise Vincenzo Montella's side are a very difficult obstacle in our path."
