Jay was at Columbia University Tuesday and addressed the video TMZ Sports first posted Sunday ... showing Jay, Bey and Blue Ivy seated as Demi Lovato belted out the National Anthem. A Columbia professor asked him if he remained seated to "convey a signal," and Jay quickly replied, "It actually wasn't. Sorry."

He said Beyonce told him she was thinking what Demi must have been going through in the seconds before starting the Anthem, because, as Jay put it, Beyonce's "performed at the Super Bowl before, and I haven't."

He said they got to their seats and were laser-focused on Demi's performance, but from a business standpoint -- "We immediately jumped into artist mode."

Jay added, "I'm really just looking at the show. The mics start. Was it too low to start?" He went on to make the point he was concerned about the audio and all aspects of the show for a very good reason.

Remember, Jay-Z's Roc Nation is now producing ALL of the entertainment at Super Bowls as part of the deal Jay struck with the NFL last year. That included Demi's Anthem, Yolanda Adams singing "America the Beautiful" ... and the Halftime Show with Shakira and J Lo.

Jay said there was no need for a "silent protest" -- as some speculated they were doing -- because we were "making the biggest loudest protest of all" by selecting such a diverse group of artists to perform at the game.

He also joked about people thinking they had Blue Ivy in on the alleged protest -- saying, there's no way their 8-year-old could possibly play it cool ... especially on camera.

Also worth noting ... the Carters attend sporting events regularly -- Jay was a minority owner of the Brooklyn Nets -- and we're told they always stand for the Anthem. We found photos and video to back that up, including the 2017 NBA All-Star Game.

Sources close to the situation tell us Jay knew revealing the real reason he sat might spark new criticism from Colin Kaepernick supporters -- some of whom took Sunday's video as a sign Jay was backtracking on his "We've moved past kneeling" remark.