Irving has been under fire since he posted the link on social media last Thursday and initially defended doing so during a contentious post-game news conference over the weekend. He has since deleted the post.
The seven-times All-Star met with reporters again on Thursday less than an hour after Silver slammed him for showing a lack of remorse.
"I didn't mean to cause any harm," said Irving. "I'm not the one who made the documentary."
Irving was also specifically asked whether, in hindsight, he was sorry for the hurt his post had caused people.
"I take my responsibility for posting that," said Irving. "Some things that were questionable in there, untrue. Like I said in the first time you guys asked me when I was sitting on that stage, I don't believe everything that everybody posts. It's a documentary."
In a joint statement on Wednesday with the Nets and Anti-Defamation League, Irving said he opposed all forms of hatred. Irving and the Nets also said they would each donate $500,000 toward organizations that work to eradicate hate.
The NBA and union representing its players issued statements condemning hate speech but neither mentioned Irving by name until Silver's comments were distributed.
"Kyrie Irving made a reckless decision to post a link to a film containing deeply offensive antisemitic material," Silver said in a statement.
"While we appreciate the fact that he agreed to work with the Brooklyn Nets and the Anti-Defamation League to combat anti-Semitism and other forms of discrimination, I am disappointed that he has not offered an unqualified apology and more specifically denounced the vile and harmful content contained in the film he chose to publicize."
Irving has been outspoken on several controversial topics over the years and played in just 29 of Brooklyn's 82 games during the 2021-22 regular season due to his decision not to get the COVID-19 vaccine.
New York City eventually rolled back its vaccine mandate, which paved the way for Irving to play for the Nets full-time in late March.
The Nets play their next game on Friday against the host Washington Wizards.
