Inter needed extra-time to defeat the Viola 1-0 via Romelu Lukaku's goal.
Conte said, “The qualification was deserved and it could've come in the opening 90 minutes, because we certainly had the chances to win it.
“The lads did well, playing 120 minutes with a good tempo, intensity and organisation. I am satisfied. I'm also happy for those players who haven't featured for a while, like Aleksandar Kolarov and Andrea Ranocchia, as they proved how much they care for Inter.
“This was the best Inter side based on the choices I could make. Achraf Hakimi was running a fever yesterday, for example. I put together a strong line-up to win the game and got a strong response from everyone."
He added: “There is a positive aspect too, as the fact we won in a difficult arena like Florence will boost confidence and recharge the batteries. These lads have won eight of their last 11 games, drawing with Roma and losing to Samp, yet it never seems to be enough.
“It was important to qualify and that is an injection of pure energy into the squad."