The singer performed in NYC Wednesday for a one-night-only show, and there's footage of him going around on social media that's raising eyebrows -- specifically, a clip of him winding down one song and transitioning into the next, where he says something curious.

Check it out ... JT tells the crowd that he'd like to take this moment to apologize -- but then hits a brief pause before he finishes his thought and says ... "to absolutely f***ing nobody."

Some in the audience cheered right then and there -- but this video is NOT being well-received online in the aftermath ... for a couple reasons, depending on how you look at it.

For starters, this is immediately being perceived by many as a straight-up shot to Britney -- which is probably spot-on considering he reportedly went right into "Cry Me a River" right after this ... and everyone knows that track is famously about his popstar ex.

Of course, BS herself recently apologized to JT publicly ... well, kinda. She said sorry if what she wrote in her book made anyone feel bad -- so it was a half-apology, of sorts, to him.

The other celeb people are expressing outrage on behalf of is Janet -- and that's 'cause Thursday is the 20-year anniversary of her Super Bowl performance with him, where he pulled her boob out in front of millions ... something folks are still angry about even today.

There was a lot of controversy over this a few years ago when a doc dove into the topic in great detail, and JT ended up apologizing at the time not just to JJ, but Britney as well.