Federico Dimarco opened the scoring in the first half after good work from Ange Bonny, before Andy Diouf doubled Inter's lead midway through the second following a goalkeeping error from Michele Di Gregorio.
Francisco Conceição pulled a late goal back for Juventus, who were denied a possible stoppage-time penalty when Leonardo Bovio appeared to foul Randal Kolo Muani inside the area. Speaking afterwards, Chivu had nothing but praise for Luciano Spalletti's side despite the defeat.
"They're a good team, well coached. Pre-season matches count for little, they have quality players. A strong team that will make its mark," he said.
Asked to assess the contributions of academy prospects Leonardo Bovio and Jamal Iddrissou, who both featured, Chivu struck a measured tone about their development.
"It's my job to coach the young players and give them the chance to express themselves at their best. They need to improve and get used to the rhythm of these matches. They need to know how to do, together with their teammates, what we ask of them.
"I don't have to promote anyone, they have quality, what interests me is the reaction to mistakes, how they deal with certain opponents. All the young players made their contribution," he said.
Off the pitch, Inter continue working to strengthen the defence, with two influential figures helping push their case to Cristian Romero. According to La Gazzetta dello Sport, Lautaro Martínez, together with club vice-president Javier Zanetti, has contacted the Argentine centre-back directly in an attempt to persuade him to move to Appiano Gentile, with the pair having shared numerous successes with the national team, from the World Cup to two Copa Américas and the Finalissima against Italy.
Tottenham value Romero at around €40m, a figure Inter could feasibly work with, but the bigger obstacle is wages: Romero is believed to be seeking at least €6m a season, above what Inter Milan would typically offer, with Atlético Madrid seen as more willing to meet his demands. For Romero, a move to Inter would also mean a return to Italian football following earlier spells at Genoa and Atalanta.
Inter are also continuing to weigh up Moussa Diaby as a potential option to replace Denzel Dumfries on the right, with Chivu currently deploying converted midfielder Andy Diouf in that role. The 27-year-old, currently at Al-Ittihad, was already monitored in January, though Bayer Leverkusen are also credited with interest, and Inter are proceeding cautiously on that front for now.