The 35-year-old, who's previously starred in Broadchurch, said that when she found out her audition had been successful: "I didn't faint - I played it really cool and cried".
'You forget that if I'm the 13th there is so much to watch and catch up on - there is so much to catch up on! - there's a wealh of television to watch and to be a part of that is emotional and overwhelming'.
"It was incredibly emotional", she told 6 Music's, Shaun Keaveny.
She told the BBC that she believed getting the role would be "a blessing and a curse", and expressed the hope that media interest in her personal life would die down: "It's not very exciting", she said.
The reaction to Whittaker's casting was mostly positive - but a sizeable minority protested that the Doctor shouldn't be played by a woman. Even now, I have even done it yet, I haven't done anything, and the fans are just the most creative, enthusiastic people. "So if I get sent something it's a mate screen-grabbing something and sending it to me".
The actress admitted that as she does not use social media she had largely missed out on the frenzy that greeted her casting. In the next series, he will be replaced by Jodie Whittaker who will become the first female to ever take on the role of the Doctor in the show's lengthy history.
"The freedoms and the fun and the scale of the storylines".
The star will reunite with her former Broadchurch showrunner Chris Chibnall next year when he picks up the reins from Steven Moffat, who is departing with the current Doctor Peter Capaldi after Christmas. There's no advice you can give because no person can play this part the same and it's so freeing'. The direction he's going to take it is going to be wonderful. "Ok thanks" - really smooth - but it shook me, you can't get a job like this and not be knocked sideways, ' she revealed. "Every script I read will be brand new and something that I can genuinely say I've never done before".
"I didn't know details, but I knew there was going to be an attempt at a really brilliant reveal".