The Giallorossi ran out 2-0 winners thanks to goals from Kevin Strootman and Radja Nainggolan, with the coach impressed with the character his side showed.
The boss admitted that his side had made a slow start but, in the end, the manner of the victory augured well for the future.
"Certain features of the players' performance were different to what we usually produce and suited us," Spalletti said. "Now we have to see if we can push on from this but it's the start of us finally acquiring a character trait that we must have, which was very welcome today.
"Sure, the match wasn't great and both teams could have done more but we carried out our game plan well in the second half."
The coach acknowledged that he had shifted things around to compensate for the loss of Mohamed Salah, crediting his players for taking on a lot of individual responsibility.
"We played with five when we had the ball but always defended with four when we weren't in possession," he said. "The players decided amongst themselves who would close down the full-back. For example [Bruno] Peres would always go on the left and [Antonio} Rudiger went out to meet Keita [Balde], becoming the fourth defender.
"Peres took up a very attacking position but I must say that Emerson [Palmieri] played unbelievably well.
"We didn't settle immediately well because [Lucas] Biglia didn't afford [Diego] Perotti much space, hence why I told Radja [Nainggolan] to make up for that. When Radja finally got his bearings, we played better and it became easier for us."
Spalletti was keen to urge focus from his side, however, with upcoming Serie A contests against AC Milan and Juventus now to look forward to.
"The derby fires the imagination but we have other targets and must focus on AC Milan now." Spalletti concluded. "We've won a big match against a great side who are well put together.
"Simone Inzaghi has done brilliantly to strike the right balance.
"We need to look beyond the city walls though. Those who want to stay inside, can do so. We want to go and see what else is out there."
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