"I will simply play and do my job as best I can, to help the club I am with," Felix told reporters.
The 19-year-old, who joined Atletico last week in a deal worth 126 million euros ($142 million), is a potential replacement for the France striker who scored 133 goals in five seasons at the club.
Griezmann has already said he will leave Atletico -- he is expected to join Barcelona when his release clause, which dropped to 120 million euros last week, is activated.
Felix's transfer fee is a record for a Portuguese club and for Atletico Madrid and makes the teenager one of the five most expensive players in history.
"Regarding the amounts, as I have said, it is a question of the market and I don't understand anything about that," he said.
Felix also downplayed comparisons with his teammate on the Portuguese national team, Cristiano Ronaldo who spent a decade at Real Madrid before joining Juventus in 2018.
"He is currently the best in the world, and possibly of all time. When he was with the national team he told me about Madrid and he said he liked it a lot, but I'm here to make my own story," he said.
"Cristiano is Cristiano and I want to be myself."
Felix will go into next season waring the number 7 jersey which up until now has been worn by Griezmann.
Atletico president Enrique Cerezo said Felix had "pure talent" and predicted that he will "make history at Atletico Madrid".