Chivu has Inter well placed to win the Scudetto at first attempt after just a short spell in charge of Parma last season as his only previous senior coaching experience.
Calhanoglu told KAFA Sports: "He was already coaching the Primavera, sometimes we'd play training matches against his team. When he started working with us, the team accepted him very quickly.
"He also played for Inter, and that's undoubtedly an advantage. He gives everyone an opportunity, even the younger players.
"With Inzaghi, it was different; they have two separate philosophies."
On his controversial move from AC Milan, the Turkey international recalled: "We waited until the last minute for Milan to make an offer for a renewal, but it never came.
"Then my agent arrived and told me there was an offer from Barcelona and Juventus were also interested. But then Inter arrived, at the last minute: Inzaghi kept calling us, he really wanted me."