Four days after Juve beat La Viola 1-0 in Serie A, the northern clubs reconvened at the Juventus Stadium to play out a 1-1 draw which saw second-half substitute Mario Gomez cancel out Arturo Vidal's early opener.
The away goal gives Vincenzo Montella's men an advantage ahead of next week's last-16 second-leg clash in Florence but Conte feels his team will manage to score the goal they require having dominated the final third in Turin.
He told juventus.com: "We're disappointed with the result, but not the performance. I can't take anything away from the lads, who expressed themselves better than they did on Sunday.
"We created plenty, hit the bar and had a big opportunity with Pogba. We were also a bit unlucky because we could have scored more than we did."
Reflecting on Gomez's equaliser, which arrived 11 minutes from time, Conte added: "We lost possession in the middle of the park and the ball over the top caught us by surprise.
"Gomez did well to get it under control and beat (Gianluigi) Buffon when he was coming off his line."
Juve's veteran goalkeeper Buffon made sure to praise Germany striker Gomez, whose first season at Fiorentina has been blighted by injury, limiting him to only three goals in 10 appearances.
"They attacked the space in behind and Gomez netted. He's a great player, and not someone who's just burst on the scene," Buffon said.
"It's a shame because we were hoping to pull off the same result as we did in the league, but there's still everything to play for."
Fiorentina were UEFA Cup semi-finalists in 2008 and beat Juventus in a two-legged final to win the trophy in 1990.
But current coach Montella insists his side are not the favourites to progress to the quarter-finals on this occasion.
"Absolutely not," he told the Gazzetta dello Sport. "Juventus score all the time so it will not be easy.
"This Fiorentina side is evolving, we are designed to play a possession game and we have to keep working hard to hold onto the ball.
"Against Juve that was even more important because they're set up in a similar way, so we suffered to get the result."