Browning told Digital Spy: "It's not a regret. People love that cast so much. Kristen Stewart is just perfect in that role and I think that everyone can see that that was the cast that it was meant to be.
"I feel kind of bad for them sometimes, the way they're hounded by the media. I don't think that I could have been as strong through that as they have been."
Browning was invited to try out for the part after being described as the "favourite choice" by the novel's author Stephenie Meyer on her personal blog.
The Sleeping Beauty actress turned down the opportunity because she was "just exhausted" and "definitely didn't want to sign on to a trilogy" at the time.
Twilight star Stewart apologised last year after comparing the intense attention she receives from the paparazzi to being raped.
Robert Pattinson, who plays vampire Edward Cullen in the series, later said that he is "afraid of buying a house" because it would make it easier for photographers to harass him.
> Robert Pattinson 'wants to hit paparazzi'
> Emily Browning 'Sleeping Beauty': 'I lose myself in film' - video
Watch Emily Browning in the Sleeping Beauty trailer below: