The 18-year-old also says he does not want to be seen as the answer to Los Blancos' lack of goals in the post-Cristiano era.
"Cristiano is one of the greatest players in the history of the club, if not the biggest.
"I don't want to carry the pressure of replacing Cristiano."
Regarding how things have gone so far in his early Real Madrid career, Rodrygo is delighted with his start.
"I didn't expect everything to happen so fast, not even in my dreams," he noted.
"A few weeks ago, I was thinking of making my debut in the Champions League; I don't know how to explain my feelings after the hat-trick.
"It was definitely unique and special."