Mijatovic played for Madrid between 1996 and 1999, scoring the only goal of the 1997-98 Champions League final for them to win the club's seventh European crown.
Zidane won a Champions League himself with Madrid as a player before retiring in 2006, and then recorded the club's 11th continental triumph last May after just six months in charge in what is his first senior coaching role.
"It's very difficult to coach a club like Real," Mijatovic, who was Madrid's sporting director between 2006 and 2009, was quoted as saying by French daily L'Equipe.
"OK, you have a great team, but everyone wants to play. To handle that, to get everyone pulling in the same direction, it's a real challenge."
"Zidane arrived when the team was going through a difficult period. The squad was struggling. He lifted their heads and won the Champions League," he added.
"We know his qualities: he knows how to handle the squad, especially the stars. I see above all a man who wants to learn," Mijatovic said.
Mijatovic said Zidane is an astute observer of the game, a trait that gets reflected in his decisions during a match.
"In each match, he makes choices. There are situations in which you have to improvise, react and he does that very well: By using players in positions that aren't their own to deal with an injury or a change in the system in relation to the opponent," the 47-year-old said.
"Against Atletico, he made different changes to the ones everyone expected. He knows what he wants, he follows his own path and he's gaining in confidence. He takes decisions and that's what makes a great coach."