Chinese-owned Inter, who finished fourth last season, had looked a serious rival to reigning seven-time champions Juventus with summer signings such as Radja Nainggolan, Matteo Politano, Sime Vrsjalko and Keita Balde.
Inter sit third, but are now 14 points behind Juventus, and risk losing ground on second-placed Napoli, who are three points ahead of Spalletti's side, and play lowly Frosinone Saturday.
City rivals AC Milan, just behind in fourth, could also close the gap when they host Torino.
Mario Mandzukic's diving header after 66 minutes was enough to settle the Derby d'Italia with Inter's Roberto Gagliardini missing a golden chance after 30 minutes to help Inter to their first win in Turin since November 2012.
"We managed the game in the right way for long spells, but we're still too careless at times and sloppy," said Spalletti.
"It would have made a world of difference had we taken the lead, but we misplaced too many passes, we made too many banal and cheap errors.
"There were situations where we didn't interpret or read them property while Juventus didn't do anything wrong," said Spalletti.
"Unfortunately, Juve are smart and we are naive. They have a way of wasting five minutes after a foul."
- 'Effective and clinical' -
Juventus captain Giorgio Chiellini was imperious in defence denying Inter striker Mauro Icardi a single shot on goal as the Argentine hitman tried to add to his eight-goal tally in Serie A.
But Spalletti defended the Inter captain.
"Icardi had the game that he needed to have, he did some great work in dropping to help the team," said the former Roma and Zenit Saint Petersburg boss.
"We were only on the back foot at the end of the first half and missed two big chances - you can't miss chances like this against Juventus."
After a stuttering start to the season Spalletti's side won seven consecutive games but have now taken just four points from their last four matches, and will host Napoli on December 26.
"We go home having not got any points, but we know that we're capable of getting a lot of points. We'll see where we are in March or April," said Spalletti.
Next up is Tuesday's crucial Champions League game against PSV Eindhoven at the San Siro as they look to seal their place in the knockout rounds.
Inter returned to the elite European competition this season after an eight-year absence since Jose Mourinho's reign when they completed the first treble of Serie A, domestic Cup and Champions League in Italian history in 2010.
Since those days it has been lean times for the 18-time Italian and three-time European champions, with the only title of any sort a 2011 Italian Cup crown.
Juventus also equalled the best ever start to a campaign in the top five European leagues set by Paris Saint-Germain this season with 43 points from 15 rounds.
"It's an important three points today because it means we're one win closer to achieving our goal in the league," said Allegri.
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