The 20-year-old has been one of the club's standout players and has scored five goals in his first five games of the campaign.
"My staff and I have worked very hard with Kovacic, and I always believed he would make a step up," Mazzarri told reporters.
"He has improved a lot, tactically and technically. He moves well with and without the ball, and is calm in front of goal.
"This is the Kovacic we always expected, but at his age and with the quality he has there is still room for huge improvements."
Kovacic has won 15 caps for Croatia and played for his country at this summer's World Cup.