The director was speaking at the Toronto International Film Festival, where Snowden had its world premiere.
Joseph Gordon-Levitt plays the US National Security Agency contractor who fled to Russia in 2013 having revealed extensive internet and phone surveillance by US intelligence.
The cast includes Melissa Leo, Zachary Quinto and Shailene Woodley.
"This is a secret underworld and no one in the NSA has come forward," Stone told a press conference on Saturday.
"It's a detective story - it goes into something we don't know.
"The government lies about it all the time and what they are doing is illegal - and they keep doing it.
"This is a very upsetting story but at the same time it's a drama - it's a great combination."
'Another kind of patriotism'
Gordon-Levitt, who flew to Russia to meet Snowden in preparation for his role, said he was interested in the film's exploration of patriotism.
"It shows two different kinds of patriotism - there's the one where you're allegiant to your country no matter what. You don't ask any questions.
"But there's another kind of patriotism that is what I really wanted to show.
"The kind that he grows into over the course of the nine years we see in this story, where he does ask questions.
"That's the privilege of being from a free country like the United States of America."
Asked what he thought might happen to Snowden, Stone hoped the whistleblower might be granted a pardon by President Barack Obama.
"Mr Snowden would come back and face trial if he could get a fair trial," he said.
"Maybe the movie could help."
'A tad dull'
Early reviews have been mixed.
Variety described it as the director's "most exciting - and relevant - movie in years".
The Hollywood Reporter called "earnest, decorous, and - dare we say - a tad dull".
Snowden was "dry and uninvolving," said The Guardian's two star review, citing Gordon-Levitt's performance as the only saving grace.
"Stone has made a film aimed at breaking out Snowden's story to the masses but it's made with such limpness that a swift read of his Wikipedia page will prove far more exciting," it concluded.
The Toronto International Film Festival runs until 18 September.