Los Blancos secured the services of the Belgium international from Chelsea for a reported €100million fee in June after seven years at Stamford Bridge.
Eden Hazard was happy Real Madrid sealed a win over Granada on Saturday.
The forward, who moved from Stamford Bridge to the Bernabeu in June for a reported €100m fee after seven years with the west London side, scored his first Madrid goal yesterday and provided an assist in Los Blancos’ 4-2 LaLiga win over second-placed Granada.
"I am pleased with the win, when you play you want to score, but the crucial thing was getting the win. We are still top of the league, that was our aim," Hazard told Real Madrid TV.
"It's always difficult to get that first goal but once you get it, you have greater confidence to shoot and I hope to score lots of goals for this great club. It was important for me to score.
"It was a really hard-fought win because Granada played really well, they're a strong side and that's why they're second in LaLiga, but we gave our all throughout the 90 minutes and won the game.
"There's always room for improvement but that's three important points."