Right-wing political strategist Steve Bannon said Thursday that he did not know about Cambridge Analytica's data mining from Facebook, marking the first time the former top White House strategist and Trump campaign boss spoke publicly about the scandal.

What happened there, Bannon said, is between Facebook, Cambridge Analytica and "the professor" – meaning Aleksandr Kogan, who reportedly shared data harvested from his psychological test Facebook app with Cambridge Analytica.

Bannon was once an executive with the political-consulting firm, which is alleged to have used data mined from millions of Facebook users to create political ads that favored Donald Trump's presidential campaign and the push for Brexit. He also claims credit for the company's name.

Bannon was speaking at a conference held by the Financial Times newspaper.

The former Breitbart News boss also pushed back on the idea that Cambridge Analytica won the election for Trump.

"Here's what won it for Trump: economic nationalism" and talking in plain language to the American people, Bannon said.

Cambridge Analytica CEO Alexander Nix was suspended earlier this week after the UK's Channel 4 ran an expose which showed the executive bragging that the firm was in charge of all the data and ads for the Trump campaign. Cambridge Analytica executives also were caught on video boasting of using entrapment, fake news and psychological manipulation in its operations.

Bannon declined to comment directly on Nix, but instead zeroed in on Facebook co-founder and CEO Mark Zuckerberg, assailing the social media giant's business model.

"They take your stuff for free. They sell it and monetize it for huge margins. That's why the companies trade for such high valuations," Bannon said. "Then they write algorithms and control your life."

Referring to Zuckerberg's apologies and media interviews reacting to the Cambridge Analytica scandal, Bannon said he "sounds like a first-year associate hired in corporate development, mumbles through the whole interview, and no one asks him a tough follow-on question." He also accused media outlets of playing "patty cake" with the Facebook CEO.

Cambridge Analytica and Facebook have both denied wrongdoing.

Facebook COO Sheryl Sandberg also apologized for her company's role in the data scandal.

"We know this is an issue of trust. We know this is a critical moment for our company, for the service we provide," Sandberg told CNBC. "We are going to do everything we can."

Correction: This story was updated to correctly attribute a quote to Steve Bannon.