The 29-year-old moved to the Bernabeu from Chelsea last summer, signing a five-year contract with the Spanish giants, who could end up paying in excess of £150m for his services.
The Belgian has only managed one goal in 15 appearances for Zinedine Zidane's side, with a series of injury problems making it difficult for the attacker to settle.
However, Martinez has backed Hazard to show his class for Los Blancos once he has fully overcome his fitness issues.
"He is very sensible, calm. He is always happy. He is focused on recovering as soon as possible to miss the minimum number of games. He was very focused on recovering well and in time for the European Championship. Now all he has to do is focus on whether he can play a very important role with Madrid this season, which I am sure he can," Martinez told AS.
"He has the perfect character to be able to react as needed when there are situations such as the operation or the postponement of the Euro. He is at the perfect age to take responsibility at a club like Madrid and with Belgium, who are number one in the world. He is fully adapted to the league and Madrid. His only problem has been injuries. He has been very, very unlucky.
"Luck plays a huge role in football and he has missed more games this season than he had in seven years at Chelsea. That is bad luck and I am convinced that very soon that luck will change, and he will be able to be a decisive and stellar player."
Hazard recently said that he would be "judged" on his second season at the Bernabeu. body check tags ::