Rules as written, a potion requires concentration. See page 141 of the DMG:
In other words, you'd be stuck concentrating. I kind of get the flavour here - if you're invisible, and you get hit, you have to try to focus on the invisibility, lest you lose the magic (or, if it's a sillier game, burp it out).
honestly, though, I think the potion miscibility table is a better balancer. We've houseruled that potions do not require concentration, but that the table it always rolled on (and I've put together a slightly different table than that in the DMG, so that players have no idea of the odds of good vs. bad results).
That is a key word given "concentration" is listed under duration. Glad you pointed that out. That does indicate that for a potion that utilizes a spell effect, concentration is required.