Simone Inzaghi urged Inter to build on their strong performance against Napoli after ending the Serie A leaders' unbeaten start to the campaign.
Piotr Zielinski netted Napoli's first away goal in four league games against the Nerazzurri to open the scoring with their first strike at San Siro since April 2017.
However, Hakan Calhanoglu equalised from the spot before teeing up Ivan Perisic's header to put Inter 2-1 up at half-time, the Turkey international recording at least a goal and an assist in a Serie A match for the 10th time since his debut in 2017-18.
Lautaro Martinez seemed to have put the game out of Napoli's reach, though substitute Dries Mertens' pulled one back to overtake Antonio Vojak as the club's leading scorer in the Italian top flight with his 103rd goal.
The defending champions managed to hang on to end Napoli's 21-game unbeaten league run, taking them within four points of the top two, and Inzaghi wants more from his side ahead of a crucial Champions League clash with Shakhtar Donetsk on Wednesday.
"It was a key game for the season, although the most important one will be in three days' time," Inzaghi told DAZN.
"We beat a very strong Napoli side and we did it deservedly too. It's always going to be a struggle against Napoli, especially as they have on average the highest possession statistics in Serie A this season with 60 per cent.
"We must continue like this. We've got to focus on the Champions League next because it's been too many years that Inter haven't got past the group phase and we have a big opportunity to achieve it.
"Wednesday we have a great chance, we have some injuries but it's a moment like this for everyone. We have to move forward match after match. We have left some points because the Champions League is very important for us."
Inter had Samir Handanovic to thank for the three points after his stoppage-time save against Mario Rui in which he tipped onto the crossbar from the left-back's header at the back post.
Mertens then blasted over during a chaotic eight minutes of additional time and Inzaghi admitted he was concerned in the closing stages while explaining why Calhanoglu got to take the first-half penalty.
"We had been a whisker away from winning several of the other head-to-head clashes, so a little fear was inevitable towards the end during eight minutes of stoppages," he added.
"We had tests in training, Perisic, Calhanoglu and Lautaro took three penalties each and scored all three, so I said just decide between yourselves! Hakan is in great shape at the moment and I wouldn't have taken him off if he wasn't on a yellow card today."