A late Adrian Mutu penalty rescued a point for Fiorentina after Roma goals from Mancini and Ludovic Giuly had sandwiched Alessandro Gamberini volley.
Fiorentina goalkeeper Sebastien Frey emerged as best afield and Spalletti insisted afterwards: "It was a very entertaining game and I had fun. We saw two excellent squads battle it out openly with end to end football and a dueling atmosphere.
"I think we could have sealed up the win, we just made a couple of little mistakes. In any case, we should have scored with all the many chances that we had."
The coach admitted: "Yes we have to intensify our focus on the defensive area of the team, but we must also admit that Fiorentina's forwards today and those of Juventus on Sunday did well to finalise what they created. In truth, we didn't struggle very much."
Fiorentina boss Cesare Prandelli said: "It was a fantastic game.
"I think my lads were up to the task, especially as we were always trailing and fought back very well.
"Every three days this season we face a new test, but this was an important match. We wanted to square off against a 'great' and for 90 minutes stayed in it. If you can do that against a team like this, then you're on the right track."