Inter won 2-1, with Valentin Carboni scoring in injury-time to earn the triumph.
Chivu said afterwards: "They played a good game, a serious match. We tried in every way to score and create confusion for an organised team that defended very low, also taking advantage of the crosses with the entry of Pio Esposito.
"We believed in it until the end, I'm proud of the lads who gave their all and we brought it home.
"It's difficult to talk about formations against a team that defended in the penalty area. In the first half I liked the search for width and the attack of depth. Once we were behind we put the second striker to fill the area more."
On Carboni, he added: "I say a lot about Valentin, but I could also say about Pio Esposito, Luis Henrique and Sucic. I'm happy for Valentin, because it was the first game after the cruciate ligament injury, he worked hard to recover and seeing him happy makes me happy."