Staunton will play the Queen in the fifth and sixth seasons of the Netflix historical drama, the latter of which will be its final outing.
Discussing taking over the role from Claire Foy and Olivia Colman, the actor told This Morning that there was “pressure from every angle”.
“I am following two extraordinary actresses, but I am also following one extraordinary human being, which is the Queen,” she said.
“Because she’s so much in a lot of our lives and we know how she looks and how she sounds, of course I have to be like her as much as I can, but also I have to tell a story and a story of a day, whatever that is.”
Staunton then praised writer Peter Morgan for his “extraordinary” ability to bring the Queen’s secretive private life to the screen.
The actress added: “We have all got so much footage of the Queen doing her speeches and things like that, and the strength of The Crown has been going inside their private lives and making it as real as you can.”
Staunton will be joined in the series’ of The Crown by Game of Thrones’s Jonathan Pryce as Prince Philip, Lesley Manville as Princess Margaret, and Elizabeth Debicki as Princess Diana.
Earlier this week, reports emerged that Dominic West is being lined up to play Prince Charles during the show’s final seasons.
Season four of The Crown, in which the Queen is played by Olivia Colman, arrives on Netflix on 15 November.