Arch Manning Apologizes For Laughing at A.I. Video of Coach Slapping ESPN's Holly Rowe

Arch Manning knows he screwed up by laughing at an A.I. video of his coach slapping a female reporter ... and he's apologizing after joking about the clip on camera.

Here's the deal ... Peyton and Eli Manning's nephew mentioned the viral clip Monday during a media availability with local reporters in Austin, Texas, after the quarterback led the University of Texas football team to a comeback over Ohio State and a No. 1 ranking ... and his youth and honesty got him in hot water.

During the presser, Arch said he's seen a few A.I. edits from the game ... including one of his head coach, Steve Sarkisian, slapping ESPN's Holly Rowe during a postgame interview. Arch said, "That's a good one."

Arch laughed, then looked at the Sports Information Director and instantly knew he'd screwed up. Now, he's apologizing for "an insensitive comment."

The A.I. video was created after a postgame interview from UT's stirring comeback went viral when Sark abruptly ended the segment to celebrate with his team. In the A.I. edit, Sark strikes Holly hard in the face before running off.

Arch called the clip "hilarious" ... which, as you can imagine, disturbed quite a few social media users -- who didn't see anything funny about a video of a man slapping down a woman, even if it was A.I. generated.

Now, Arch says ... "There is nothing funny about it. It's easy to say I didn't mean it, but I know my words and actions were hurtful to a lot of people."

Arch personally apologized to Holly ... "I have a ton of respect for her and appreciate her showing me grace in this moment."

The 22-year-old, who projects as a future NFL first-round draft pick, finished off his message ... "I need to do better and will be more thoughtful going forward."