Hazard made a subdued start to his Madrid career with an appearance as a second-half substitute in a 3-2 win against Levante at the Bernabeu.
The Belgium international, who joined Madrid from Chelsea in June, has only recently returned to training following a thigh injury.
Hazard showed a few nice touches after he came off the bench in the 60th minute, although the 28-year-old forward was far from his sparkling best.
"When he touches the ball he has a lot of versatility," Zidane said.
"But what he needs now is to train more. He has only done four workouts with the team.
"The second half was more complicated for us, especially at the beginning. When the opponent scores a goal after three minutes it is difficult.
"But we got three points. We must not look for excuses, the important thing is to keep the first part of the game and play more minutes as the first part. We can improve a lot, we have to play better."
Real seemed to be cruising victory against Levante after two goals from Karim Benzema and one from Casemiro put them 3-0 up at half-time.
However, Borja Mayoral, on loan at Levante from Madrid, and Gonzalo Melero reduced the deficit.
Madrid’s defensive shakiness almost allowed Levante to take a point and the capital giants have yet to keep a clean sheet this season.
Zidane was full of praise for Benzema, who took his tally to four goals in four LaLiga matches, but acknowledged the need for an improvement from his struggling backline.
"What I can say about Benzema is keep it up," Zidane added. "We are very happy to see Benzema like this. We have seen Karim's ovation from the supporters.
"The defence? It doesn't worry me, although we have to improve and we are going to do it.
"Physically, maybe, the international break could be noticed but I don't want to look for excuses.
"I know we are going to score more goals and concede less."