The FBI announced Friday it had concluded that North Korea, whose leader Kim Jong Un is assassinated in the film, was responsible for the attack.
"We cannot have a society in which some dictator some place can start imposing censorship here in the United States," he said. "Because if somebody is able to intimidate folks out of releasing a movie, imagine what they start doing when they see a documentary that they don't like or news reports that they don't like."
"Or even worse, imagine if producers and distributors and others start engaging in self-censorship because they don't want to offend the sensibilities of somebody's sensibilities who probably need to be offended," he continued. "So that's not who we are. That's not what America is about."
The president also referenced the running of the Boston marathon a year after the attacks there.
"We can't start changing our patterns of behavior anymore than we stop going to a football game because there might be the possibility of a terrorist attack. Any more than Boston didn't run its marathon this year because of the possibility that somebody might try to cause harm. Let's not get into that way of doing business."
Obama added that he wish Sony "had spoken with me first" before pulling the film, which starred Seth Rogen and James Franco. He also pledged a response.
"They caused a lot of damage, and we will respond," he said. "We will respond proportionately and we'll respond in a place and time and manner that we choose."