Gaetano Castrovilli struck the winner in the 1-0 triumph.
Iachini said, “I always ask Castrovilli and the other midfielders to be more present in the box and be ready to finish off the chances. They have it in their capabilities and we hope they do it more this season.
“Chiesa was meant to give width to the team, so we'd go around the Torino defence, and it worked better in the second half. We are still helping some new players to settle in, we take it one game at a time and try to grow.
“Towards the end of last season, we had a very solid defence, but at times we need to finish our chances better. I liked the overall attitude, which was courageous and positive."
The coach was asked if he believed Fiorentina would compete for a place in Europe this term.
“We finished 10th last season after I took over with us fourth from bottom. We need to be more consistent, try to get as many points as possible and take it one step at a time. If you want to climb a mountain, you can't sprint, it has to be one step at a time."