La Viola claimed a 1-0 win on Sunday night thanks to Milan Badelj's late low drive, ending the Giallorossi's 20-match unbeaten run in Serie A.
Roma created more chances and enjoyed more possession at the Stadio Artemio Franchi, but a cutting edge in front of goal proved elusive as Badelj's 82nd minute finish snatched the three points.
“This defeat hurts because we deserved more than we got," Spalletti said. "Things didn’t go our way today.
“We have to accept the result but be satisfied with our performance. My players did their duty today.”
He added: “It was a good match between two good sides. We needed to be more clinical when we were in control of the game. We had three or four moves which we should have turned into great chances.
“We didn’t play as well in the second half. We lost too many easy balls – that’s something we’ve been doing too much recently. We weren’t incisive enough when we had the ball at our feet. We got stretched and then we weren’t able to hit the same levels of consistency as we did in the first half. “
“Overall, it was still a good performance despite the result.”
The result means Napoli sit top of Serie A TIM on 10 points, with Roma (seven points) among a number of sides bunched at the top after four games.
“The table is really tight but this defeat is a missed opportunity for us," Spalletti said. “When you lose you go home with no points but you still have to evaluate the performance. The team did its job tonight. Sometimes in football you end up losing when you play good teams like Fiorentina.”
Fiorentina's goal was somewhat controversial, with Nikola Kalinic perhaps in an offside position - and interfering with play - as he stepped over Badelj's strike on its way towards goal.
“Wojciech explained in the dressing room: he had to take a step to the left to see the ball and then the goal went in on the side he’d left open," Spalletti revealed. "We just have to focus on what we can affect. It’s a tough defeat to take.
"The team didn’t deserve to lose after the way they played. They deserved at least something, even if that was a draw. We played well in the first half, as did Fiorentina. The little things didn’t go our way tonight.”