Flares were thrown from the Croatian contingent midway through the second half at San Siro, halting play for about 10 minutes.
The Croatians had the best chance to win after the restart, with Ivan Perisic dragging a shot just wide of the target with Italy goalkeeper Gianluigi Buffon stranded.
But Kovac was concerned by the behaviour of the visiting fans, who irked him once more.
"I feel I need to talk about the off-field incidents," Kovac said.
"I am very disappointed about our supporters' behaviour - something which had already happened in Switzerland in a previous match.
"That's why I wanted to say sorry to everyone for their behaviour and actions.
"I have already said sorry to those on the pitch, the referee and the Italian players but I wanted to do it again here.
"I am truly sorry for our fans' behaviour."
Kovac said his side were unfortunate not to take all three points and preserve their perfect qualifying campaign, as they remained level with Italy on 10 points in Group H.
"I think that we basically controlled the game for the full 90 minutes," Kovac said.
"Italy were good in defence but they still left some gaps behind and we had more chances than Italy at the end.
"I remember especially a good chance for Ivica Olic in the first half and then with Perisic in the second which would have given us the full three points.
"I am a bit disappointed because it feels like two points dropped for us."
