Massimiliano Allegri's Napoli twice held the lead before Inter fought back to win, a result that keeps Chivu's side firmly in the early title conversation.
Speaking to DAZN, Chivu praised the spectacle the two sides had produced.
"A great game to watch, entertaining, a great advert for Italian football. Two teams that played with an open face, without thinking about protecting the result," Chivu said.
"There were plenty of chances at both ends — in the end we win, but credit has to go to Napoli, because they're a strong team with players who make the difference, and well coached."
Asked where his side could have done better, Chivu pointed to the manner of the goals they conceded.
"We could have managed the first goal we conceded better, and the second was a consequence of that ball not going out of play. But I liked the reaction — the team didn't fall apart and raised the tempo, going vertical," he said.
"The 2-1 gave us a bit more hope, we made a few changes and in the end we were rewarded for our courage too. In the final minutes it was bedlam, the crowd pushed us on so much that we couldn't communicate with the players to tell them how to set up."
Allegri, whose Napoli side led twice before being pegged back, struck a rueful tone afterwards.
"For the spectators and for Inter it was an entertaining match, for us a bit less so. We were too careless at 2-1, and then they're a strong side and they changed the tempo, causing us problems," he said.
Pressed on his biggest regret, Allegri pointed to missed chances at the other end.
"That's football — we could have scored and instead they did, and they won the game. There's room to improve, both in our overall performance and how we managed the ball. Even in the first half we had good situations but didn't score, and they're very good at creating chances out of nothing," Allegri said.
"We need to stay calm — right now we're paying too heavily for our mistakes. The team's condition will certainly improve, but now we have to think about the Champions League."
The result leaves Inter Milan well placed in a Serie A title race that both managers agree remains wide open, with the two sides having produced one of the more compelling contests of the season so far at San Siro.
Chivu was also asked about a knock picked up by full-back Federico Dimarco during the match.
"I don't know, we've got two days available. We'll see," he said.