Udinese raced into a shock lead through James Abankwah and Jurgen Ekkelenkamp inside the opening 16 minutes, but Inter hit back before half-time through Carlos Augusto and Nicolo Barella, then took over after the break. Marcus Thuram, Francesco Pio Esposito and Ange-Yoan Bonny added three more in the second half before Noah Gueye's late consolation set the final score at 5-3, lifting Inter Milan level with Roma at the top of Serie A.
Speaking to DAZN, Chivu pointed to the strength of his squad as the reason his side were able to recover from such a difficult start.
"This is the way, because the season is long: we play every three days and need everyone," Chivu said. "Thank God we have a competitive squad, with great players. Our job is to get them ready, even those who arrived late and missed pre-season, and to keep everyone happy because they need to feel part of the project. Last season taught us we need everyone.
"Today I saw Bonny happy, finally off the mark. I saw Mkhitaryan start again, and Stones started too. We need to find the right balance in keeping everyone satisfied, because they're all excellent players who will help us during the season."
Asked about John Stones, withdrawn during the match, Chivu said he had not yet spoken to the defender.
"I don't know, I haven't had the chance to talk to him. I think he felt something in his flexor, he'll probably need tests."
Pressed on why Inter keep falling behind, Chivu pointed to individual errors rather than a deeper issue.
"It comes down to individual mistakes, and those are much easier to fix," he said. "I'm not worried, except for what I wasn't able to get across about our approach during the week. We started flat, without any spark, and had to react at 0-2. This team has it in its DNA to find its pride and do the things it should have done from the start."
For Udinese, head coach Kosta Runjaic pointed to the scale of the challenge Inter present rather than any tactical failing.
"Inter had 65% possession against Real Madrid and scored three goals against Napoli in half an hour," Runjaic said. "Our strategy was to show our spirit, and we managed that until it was 0-2. Their first goal, with a great strike, changed the game. They are an extremely strong team who've strengthened further, and they played with huge energy. We fought, but our level wasn't good enough today. We were also missing several players, but we have to accept the defeat."