Mauro Camoranesi opened the scoring and David Trezeguet secured victory, although Inter midfielder Nuno Maniche's effort gave Juve a scare.
"We played with depth and desire, that is important. We wanted to win and we achieved that," beamed Ranieri.
"We struggled in some instances, but when there is an open game then we are right in there. When there are teams that clam up, either we find a moment of brilliance from an individual champion or we're in trouble.
"Camoranesi has quality and is a wonderful player. Sometimes he holds on to the ball too much, but in some circumstances he takes the pressure off the team, dribbles past people and earns free kicks. He fits in well with Momo Sissoko."
Alessandro Del Piero did not score, but he set up Trezeguet's goal and was denied on several occasions by Julio Cesar.
"He trains with his own fitness Coach and then he trains with us. He knows how to deal with his own body and can also talk with me in a relaxed manner. Ale believes in this project and the champions like him set a great example for the younger players."
Camoranesi's opener was offside and Inter coach Roberto Mancini lamented: "There's not much I can do about it now, these things happen. At least they won't say we're favoured by referees anymore."
He continued: "The fact we have lost so many players is something we are paying the price for. We must not have regrets over this game, as it is behind us now."