The former Chelsea man scored his first goal in his sixth appearance for Los Blancos but was more pleased with a win that keeps them top of La Liga
Eden Hazard believes breaking his duck for Real Madrid will give him more confidence, but said team wins are more important than personal glory.
The former Chelsea star moved to the Santiago Bernabeu in the summer in an £88 million ($112m) deal but had struggled to settle, partially due to injury.
He opened his account for Los Blancos in his sixth appearance with a wonderful lob in their 4-2 win over Grenada.
“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 today.
“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 today.”
Granada are surprisingly in second place and a win would have taken them into the international break ahead of Real.
Although the final scoreline looked comfortable, Granada gave Hazard’s team a scare, bringing the game back to 3-2 from a 3-0 deficit before an injury-time James Rodriguez goal sealed the three points.
“It was a really hard-fought win because Granada played really well,” the 28-year-old said in praise of Saturday’s opponents.
“They’re a strong side and that’s why they’re second in La Liga.
“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.”
Madrid are now guaranteed to head into the international break at the top of the pile in the Spanish top flight, but Granada could be passed by several clubs, including Barcelona and Atletico Madrid, who play on Sunday.