Kushner's assessment marked his first public comments since the release of special counsel Robert Mueller's report last week.
Mueller's report concluded that the Russian government interfered in the 2016 presidential election "in sweeping and systematic fashion."
The interference included both a social media campaign that favored Trump and disparaged Democrat Hillary Clinton, and the hacking of computers maintained by allies of Clinton and the subsequent releases of stolen documents.
The report did not find sufficient evidence to bring charges of criminal conspiracy with Russia against Trump or anyone associated with his campaign. It did not offer a conclusion on whether Trump obstructed justice.
Attorney General William Barr later concluded that there was not sufficient evidence for obstruction of justice, but House Democrats are continuing to pursue that issue.
When asked Tuesday why the Trump campaign did not reject Russian attempts to get close to the campaign, Kushner said, "We didn't know that Russia was doing what they were doing."
"The notion of what they were doing didn't even register to us as being impactful," he said, adding: "When the whole notion of the Russian collusion narrative came up, I was the first person to say I'm happy to participate with any investigations. I thought the whole thing was kind of nonsense, to be honest with you."
Shortly after Kushner's interview, which was streamed live, Trump took to Twitter to praise his son-in-law.
"Great interview by Jared," he wrote. "Nice to have extraordinarily smart people serving our Country!"