Juve won a thriller 4-3 with Vasilije Adzic hitting the winner in injury-time.
Chivu remarked afterwards: "I saw a lot of quality, a lot of determination. I take credit for the performance and what we showed from the start despite going behind twice. It's never easy for anyone in this stadium. We should have handled the final ten minutes differently, but we have to build on the good things we showed today."
On Hakan Calhanoglu's goal, which was created in training, he said: "When you're facing a low block, shooting from outside the box is an option. I'm happy for him because he's an important player for us; he's overcome certain moments. I'm appreciative of the team's performance, which remains strong; they just need to learn to manage certain things to bring home important results."
On Inter's character, with the players never giving up, Chivu added: "The performance remains, I'm happy. Unfortunately, there's also the disappointment of not taking anything home, but we bring the knowledge that by fixing small things we can get some satisfaction in the immediate future.
"Then now we have the Champions League, which gives us the opportunity to turn the anger into something positive, to better understand the moments of the match, especially when you've worked so hard to turn it around."