Hazard's thunderous strike in the first half against Huesca, his first goal for the club for 392 days, set Madrid on their way to a 4-1 victory on Saturday.
The Belgium star described it as a "beautiful goal" in a social media post but surprisingly did not celebrate with much aplomb when the ball hit the net.
Head coach Zidane did not feel there was much to glean from Hazard's reaction, though.
"I'm happy for his game," Zidane said. "He played 20 minutes the other day, and now more.
"We know the quality he has; he scored a good goal. We needed it in the first half because then the game was different after the goal.
"You can see associations between players. Hazard plays on the left and Vini's [Vinicius Junior] preferred position is on the left. We'll see how we do things.
"He's okay, he has no problems, [he is] happy. He's happy for his goal and his team-mates are happy for him.
"It's a win, four goals, and you have to be happy."
Hazard's thumping effort broke Huesca's impressive first-half resistance before Madrid assumed control through a Karim Benzema double and a Federico Valverde goal.
The win sent the champions back to the top of the table, two points ahead of Real Sociedad, and served as a useful response to a disappointing Champions League performance at Borussia Monchengladbach in which they snatched a 2-2 draw after falling 2-0 down.
"It was like a final. We had to get three important points and we did," Zidane said.
"The game wasn't perfect, but there are four goals. It's always said that we don't score, that we don't play well... and since the situation is a bit strange, we need a lot of energy from among ourselves because what comes from outside doesn't help.
"We more or less controlled their strong points. From there, we had... not the best game, but after two games last week, where we put in a lot energy, we have to be happy.
"We know we can do better and that's what we're going to try to do."