"These are the classic matches where, if you don't close them out, you can run into trouble. In the final minutes we came apart, going into confusion and putting ourselves into a panic. But we held on," Chivu said.
"We created a lot - if there's a regret, it's not converting the chances we had. We knew how to suffer right to the end, even if that's not ideal because it lacks continuity.
"All things considered, given where we are and the fitness we still need to find, we leave Cagliari with three points and some extra minutes for lads like Akanji, Lautaro, Calhanoglu and Thuram.
"You can see Marcus is a bit behind, and Jones too. Now the season's started, unfortunately we have to think about getting those who were at the World Cup back up to speed. We're happy with the win, with a little regret over the missed chances."
Asked whether he now feels he has more tactical options than last season, Chivu pointed to in-game improvisation.
"Today I had to adapt Pavard to a wing-back role and put Bisseck in the middle because I sensed the moment needed it. Then he made a great goal-saving tackle. I'd also have liked to have shown more personality, like in the first half, but it was a moment of confusion and I had to react accordingly."
On his new English contingent, Chivu urged patience.
"It's still early, they've only just arrived. They have quality and experience - Stones and Jones come from City and Liverpool, playing in stadiums with that kind of pressure is second nature to them, and we're hoping that shows.
"But they need to find their fitness, and in Jones's case, also the personality and courage to adapt to how we play. In terms of attitude, though, there's nothing to criticise."
He confirmed his own input shaped the summer's recruitment: "We lost five players and had to replace them. We needed a centre-back and Stones arrived, a right wing-back after losing Palestra and Khalaili. Diouf is showing good signs of progress there too, and we chose a more defensive profile in Spence who can play on either side.
"In midfield we'd been thinking about Jones for a while, for his quality, intensity and composure. We have some really good players in there - it's on me to pick the best and keep everyone happy, which is the hardest job for a coach with a competitive squad."
Asked about Inter's Champions League draw against José Mourinho's Real Madrid, Chivu was already looking ahead.
"I thought about Napoli, since now I have to go to Madrid after playing there. Tonight we knew Cagliari wouldn't be easy - Juventus and Roma both lost points here last season, and others struggled too. In Madrid we'll compete - it's eight Champions League matches and we want to be competitive. We know exactly what score we need to reach to avoid the play-off."