Carlos Augusto struck in the 77th minute, finishing Henrikh Mkhitaryan's pass to give Inter the lead nine minutes after Bastoni was sent off for a second yellow card. The hosts then had to withstand sustained pressure, with goalkeeper Josep Martínez producing two important saves late in the match.
Chivu was relieved to secure a result after Inter Milan's difficult start to the league phase, having lost their opening matches against Real Madrid and Club Brugge.
“I think what happened in the Champions League last year has left its mark. We had lost two of our first eight matches, and six remained. The pressure increases because you cannot afford mistakes,” the Inter coach said.
He praised his players for responding to the challenge, particularly after going down to ten men.
“I saw a team that started well and then became intimidated. The three substitutions gave us energy, we found the right runs and what we needed. We also found some calmness. When we were reduced to ten men, we understood that we had to make an extra effort,” Chivu explained.
The coach highlighted the importance of accepting difficult moments rather than relying solely on attractive football.
“We need humility to accept that playing beautifully is not enough. You have to get your hands dirty and do everything necessary. I saw important runs even when we were down to ten, and we accepted that we had to suffer,” he added.
Chivu also addressed Bastoni's dismissal, describing the incident as a moment of naivety and warning that players must manage their frustration more carefully.
Shakhtar coach Arda Turan, meanwhile, was disappointed that his team had failed to take advantage of their numerical superiority.
“If one team beats you, it means they have done better, so I congratulate them. We have to learn how to play against great teams,” Turan said.
He believed Shakhtar had competed well before Inter were reduced to ten men, but the change in circumstances allowed the hosts to exploit spaces on the flanks.
“Eleven against eleven, our timing was right. When they were down to ten, spaces opened up on the wings. We suffered from their transitions. We do not accept this result,” the Shakhtar coach added.
Inter's winning goal came from precisely that situation, with Mkhitaryan releasing Augusto on the counter-attack. Shakhtar were unable to find an equaliser despite their late pressure.
For Chivu, the victory offered encouragement after a difficult European start, while Turan was left to consider how his side could become more effective against experienced opponents.
Inter now have renewed momentum in the league phase, but Chivu's message was clear: the work rate and willingness to suffer shown against Shakhtar must become a consistent feature of their performances.