The actress was asked by ShortList if she 'hovers' over the web to see what people say about her being picked for the role.
"I wouldn't say hover, but I definitely looked it up," she said.
"It affects me and I think about it, but there are years' worth of comics and so many different versions, so you just hope for the best and try to sleep at night."
Of how she deals with her increasing fame, she added: "It depends on my perspective that day.
"I'm not being harassed and I still have a relatively normal life. I was walking around London the past few days; nothing."
Stone recently described comic books as "recent mythology" which can be told "many times".
The Amazing Spider-Man - London premiere pictures: