Two goals in three minutes from Ivica Olic and Milan Rapaic handed Jozic's team a victory few expected them to achieve.
And the win seemed even more unlikely after Croatia's poor opening game performance in their defeat against Mexico which led to Jozic dropping Davor Suker and Robert Prosinecki.
"It was diehard football against a tough Italian team. I am glad my players played just how I asked them to do," said Jozic.
"All I can do is point out the heart of my players. They were sport heroes in tonight's match. In the last 20 minutes we had three injured players and I didn't know what to do.
"They were dying for each other on the pitch."
Jozic said passion was the key to Croatia's success.
"It was the decision of my team not to give up and an important moment was when we equalised and after that we decided to attack.
"Usually I like to praise individuals, but today would be a big mistake to name one player."
Ivica Olic, who scored Croatia's equaliser, expressed his delight at the victory.
"This victory goes out to the entire Croatian nation. With the two goals in the second half we deserved the victory."