Sony Entertainment CEO Michael Lynton fired back at President Obama today after the president said the company had "made a mistake" by pulling The Interview, saying in an interview with CNN's Fareed Zakaria GPS that "we have not caved."

During his year-end press conference this afternoon, the president acknowledged the "significant damage" dealt to Sony Pictures by a cyber attack on the company in late November — an attack that the FBI said today was carried out by the North Korean government — but said Sony shouldn't have canceled The Interview's release in response.

"I am sympathetic to the concerns that they faced. Having said all of that, yes, I think they made a mistake," said Obama, adding that if Sony had consulted him first, he "would have told them, 'Do not get into a pattern in which you are intimidated by these kind of criminal threats.'"

Asked by Zakaria if he was disappointed at the president's remarks, Lynton replied, "I would be fibbing to say I wasn't disappointed."

Lynton told Zakaria that "the president, the press and the public are mistaken as to what actually happened." He went on to lay out a timeline of events from Sony's point of view. Sony spent the weeks following the attack "trying to keep our business up and running, and get this movie out into the public," said Lynton. But once the hackers issued a threat against theaters that would dare to exhibit The Interview, major U.S. theater chains came to Sony "over the course of a very short period of time" and told the company they would not carry the movie. In response, Sony decided to pull the film.

"We do not own movie theaters. We cannot determine whether or not a movie will be played in movie theaters," said Lynton. "At that point in time, we had no alternative but to not proceed with the theatrical release on the 25th of December."

He continued, "We have not caved, we have not given in; we have persevered, and we have not backed down. We have always had every desire to have the American public see this movie."

Regarding the suggestion that Sony release The Interview digitally, Lynton said the company continues to explore its options, but noted that no "major video on demand distributor" has been "willing to distribute" the film. Sony does have a video on demand service of its own, Crackle.

The Interview, which stars Seth Rogen and James Franco and was directed by Rogen and Evan Goldberg, focuses on a television host who is recruited by the CIA to assassinate Kim Jong-un, the leader of North Korea. CNN will air Zakaria's full interview with Lynton tonight during Anderson Cooper 360, and Sunday on Fareed Zakaria GPS. You can see two clips from the discussion below.