APOEL stunned the Viola 2-1, with Anastasios Donis and David Abagna scoring for the hosts before the break, with Jonathan Kone hitting Fiorentina's goal midway through the second-half.
Afterwards, Palladino denied taking the game lightly.
Performance:
"We knew that today we could face a team with a very low block. They played 4-1-4-1, only using counterattacks: we prepared the game well, in the first thirty minutes we had control and we created situations to hurt them. We were naive in allowing counterattacks.
"And once we were behind it wasn't easy: we put them there but without finding the final spark and breaking them down. They played to ruin everything, even in an impetuous manner. In the second half we almost never played, they broke the rhythm. Let's analyze what we did well and with great balance we immediately think about the championship."
The ferocity you spoke of yesterday was not seen:
"Sometimes we were light, between controls and passes. And we were unable to break the passing lines. They defended themselves tightly and closed, it wasn't easy, but the counterattacks we took were due to our mistakes. There was some light-heartedness and we must not commit it. They spat blood to win, with great intensity and desire, when we face teams like that we have to put in something more."
Did you underestimate APOEL and the Conference League?
"We didn't underestimate anything, absolutely. We care about the Conference, we want to finish in the top positions and we care about a European competition. Those who took to the field today wanted to prove their worth and if I could go back I would make the same choices. The lads trained really well during the week, I had no signs that we could lose. Often these matches are decided on incidents and they turned them to their advantage."
The next match you will face another Cypriot team, Pafos. How will you face them?
"With the same mentality but trying to put a little more into it."
How do you rate the adaptations of Richardson and Parisi?
"In my opinion Richa moved well, finding spaces was not easy. They had a fixed man there to take our attacking midfielder. We know that he is a ball-handler and does not attack the depth, in my opinion he did well and we could see him again. Fabiano had a good performance, he worked well on the chain even if, we know, he is not a natural winger. However, he also did well when he moved to play as a fifth."