The Scudetto holders got off to a great start at the Juventus Stadium on Thursday in the first leg of the sides' last-16 tie as Arturo Vidal broke the deadlock inside three minutes.
Conte's men, who beat Fiorentina 1-0 on Sunday in Serie A, looked set to take a slender lead into the return game in Florence next Thursday but Mario Gomez restored parity with 11 minutes to go.
Despite the late disappointment of the former Bayern Munich striker's goal, Conte remains upbeat about Juve's chances of progressing past their Serie A rivals and into the last eight.
"I am always optimistic," he told reporters afterwards. "It's a football match, we play to win and we have won a lot, but it's fair to draw against Fiorentina, as they are a strong side.
"I do feel we were a little unlucky, as we could've scored more.
"In all honesty, I preferred this performance to Sunday. Of course, when you concede a goal it's hard to justify, but I feel the team created many chances, hitting the bar as well and probably expressed better football than we saw on Sunday.
"When you concede a goal there are always situations to analyse and corrections to be found. We lost the ball in midfield and this through-ball took us by surprise, then Gomez did very well to control and beat [Gianluigi] Buffon as he came out."
Juve have not been convincing against Fiorentina this season as they lost 4-2 away after going 2-0 up before almost letting a one-goal lead slip at the weekend, but Conte believes the visiting Viola earned their draw with the Bianconeri.
"Maybe we shouldn't take the lead!" joked Conte. "On a psychological level, teams have a different approach, maybe subconsciously, when going in front early on. We have gone in front in every game with Fiorentina this season.
"The 4-2 defeat was strange, as they scored four in 20 minutes. It's true on Sunday that Fiorentina pushed hard in the final stages, but I felt it was a deserved victory.
"If we look at the chances created on Thursday, then I'd say we were a little unlucky to draw. It was a good performance from both Juventus and Fiorentina, so I don't see why we should praise one side to the detriment of another.
"It was a great game and a fine advert for Italian football in Europe. I imagine those watching enjoyed the spectacle."