"This is like the President retweeting the Ku Klux Klan. This is not a mainstream organization and for the President of the United States, our greatest ally as a country, to be retweeting, to be providing a microphone to those voices," Cox told CNN's Anderson Cooper on "AC360."
"I think no matter what your perception of the UK, I think has been shocked by that."
The videos, posted by Jayda Fransen, the deputy leader of Britain First, a far-right and ultranationalist political group, depict purported Muslims assaulting people and, in one video, smashing a statue of the Virgin Mary.
"These narratives have impact," Cox said. Cox's wife, a member of Parliament, was killed in June 2016 by a 53-year-old man with extreme right wing views as he shouted "Britain first."
"When you retweet and endorse an organization like this, what that does is it changes people's views of what is acceptable," Cox said. "It means that people are more open about their hatred. It means they're more likely to act on their hatred."
White House press secretary Sarah Sanders defended Trump's retweets, telling reporters he shared them to start a conversation about border security and immigration.
"I think his goal is to promote strong borders and strong national security," Sanders told a small group of reporters after appearing on Fox News.
Sanders also downplayed questions about whether the videos were authentic, because "the threat is real."
Cox slammed Sanders' response, calling it "an absurd justification."
"I'm sure she has the hardest job of anybody in the world," he said. "But I think even in the list of desperate attempts to defend something that was indefensible this was a pretty pathetic attempt at doing so."
Cox went on to describe his wife as a humanitarian who cared for her constituents and would be disgusted by the President sharing anti-Muslim content.
"She would have been, if she was still here, as outraged I think as anybody that the President with whom we should have an incredibly close relationship is actively undermining our cohesion as a country -- is actively supporting this extremist group I think she would be horrified by."
"Of course we can disagree about the role of Islam in our society," Cox said. "We can disagree about immigration. We should be able to disagree about all of these things and still say that hatred has no part in our society."