(CNN) Steve Bannon said his former colleague and top White House economic adviser Gary Cohn should have resigned after publicly rebuking President Donald Trump for his response to racial violence in Charlottesville, Virginia.

"I'm obviously talking about Gary Cohn and some other people, that if you don't like what he's doing, and you don't agree with it, you have an obligation to resign," the former White House chief strategist told CBS' Charlie Rose in an interview for "60 Minutes." A clip aired Thursday morning on CBS's "This Morning."

"So Gary Cohn should have resigned?" Rose asked.

"Absolutely," Bannon said.

Bannon discussed his loyalty to Trump in the context of the Charlottesville fallout, saying, "My problem -- and I told (White House chief of staff John Kelly) this -- was when you side with a man, you side with him. I was proud to come out and try to defend President Trump."

The controversial ex-Trump aide also reiterated many of the themes Trump himself articulated in response to Charlottesville.

"He's talking about the neo-Nazis and the neo-Confederates and the Klan -- who, by the way, are absolutely awful, there's no room in American politics for that, no room in American society for that -- and all Donald Trump was saying was, 'Where does it end? Does it end at taking down the Washington Monument? Does it end in taking down Mount Rushmore? Does it end in taking down Churchill's bust, out of the Oval Office?'"

Bannon also explained how he sees his role now that he's outside the White House, describing himself as a "street fighter."

"Our purpose is to support Donald Trump," he said.

"And destroy his enemies?" asked Rose.

"To make sure his enemies know that there's no free shot on goal," Bannon answered.