The Romanian head coach, speaking to Sky Sport Italia, was candid about a difficult first half before Inter found their rhythm after the break.
"In the first half we struggled a little in possession. We were slow and Cagliari occupied the pitch better. In the second half we raised the intensity in our play, unlocking the game. This team, when it goes ahead, removes some pressure from itself and starts to enjoy playing."
On the mood in the dressing room, Chivu offered a sharp observation.
"I don't see them often because they're always on their phones. There is an awareness of everything that has been done well to be competitive. With five games to go we have achieved Champions League qualification."
Asked how far the squad was from being truly competitive in European competition, Chivu was measured.
"These players have left behind what happened last season — it wasn't easy, but they put themselves on the line. Playing in the Champions League is not simple. You face top-level teams, especially the English sides who spend enormous amounts of money. We want to be competitive there too — it's one of the club's objectives."
On his own contract situation, which runs to 2027, Chivu said he had not discussed it with the club.
"I was only focused on achieving qualification for next season's Champions League. I prefer to stay focused on the pitch and not on the future."