Hazard joined Madrid in preseason from Chelsea in a deal that could reportedly cost up to €140 million (£124 million/$153 million) but a thigh injury suffered last month has proven an early disruption, goal.com reported.
Coach Zinedine Zidane stressed the need to be patient with Hazard as Real was desperate to avoid aggravating the injury before handing him a first start against Paris Saint-Germain on September 18.
But the Belgium international mustered just a single off-target shot and one key pass as Madrid was swept aside with ease at the Parc des Princes, PSG winning 3-0.
He was similarly unspectacular in the subsequent games against Sevilla and Atletico Madrid – either side of being an unused substitute for the win over Osasuna – and Hazard recognizes he is yet to earn the right to be regarded as a 'Galactico'.
"I am not yet a Galactico, I have to be the one to prove that I can be out on the pitch," he told reporters ahead of the Champions League clash with Club Brugge on Tuesday.
"We all know the history of the number seven jersey in this club and I have to be the one to prove that I can be the best in the world.
"I want to enjoy myself on the pitch, give the maximum, not only in games but also in training. I don't doubt myself, I don't doubt my coach. It's all a matter of trust.
"I'm confident and sure everything will work out fine.
"The criticism doesn't affect me. I haven't noticed much. I know when I work to the fullest, everyone expects me to score three goals in each match.
"I think I can do better, I am also critical of myself, but working every day. Maybe I have a little delay because of the injury, but I am 100 per cent.
"I now have to demonstrate my level and improve so the fans are proud of me."