Benzema is already up to 10 strikes in 18 games this season, well on track to break the 20-goal barrier for the first time since 2015-16.
Madrid have felt the absence of Ronaldo, who was consistently prolific at the Santiago Bernabeu and finished his career as the club's all-time record goalscorer before leaving for Juventus in July.
Benzema, whose best haul for Madrid was 32 goals in 2011-12, said he needs to take more responsibility after the loss of Ronaldo.
"A little bit more now that Cristiano has gone; now he's not here to bring us goals so it's up to me to do that," he told Real Madrid TV.
"I feel very motivated and I'm ready to take on the task."
Under new boss Santiago Solari, Madrid have recovered from a poor start to the season, now sitting just four points behind La Liga leaders Barcelona despite being in sixth.
Benzema, 30, said the club has always demanded more from him, and he is eager to deliver.
"They always ask me for more," he added. "Madrid is the best club in the world. Everyone always wants more from a striker – more goals, more touches, more assists, it's normal.
"I'm more motivated than ever to make it a great year for us."