The France international struggled towards the end of last season and has netted just once this campaign, with Real losing two of their opening three La Liga matches.
Along with captain Iker Casillas, Benzema was jeered and whistled at during Real's 2-1 loss to Atletico Madrid on Saturday.
Zidane, coach of Real Madrid's reserve team, said the 26-year-old understood he needed goals.
"He's the main striker at Real Madrid but he has not scored recently. The critics will always be there," Zidane told RMC Sport.
"He must score with Madrid and with France and he is aware of that. He knows the kind of player he is and he knows what is expected of him.
"Last year I was closer to him but now a little less so because I'm busy with Castilla [the reserves]. In the next game he will score and we will move on to something else."
Zidane was linked with the coaching job at Bordeaux in pre-season before the move fell through.
The former France international said he still had the desire to coach at the top level.
"I want to continue with Castilla this year and then we'll see," Zidane said.
"I have ambition and I have an objective to take charge of a team in the top division. To look after a group like this is hard work."
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