Can I say this:
I forgot about it minutes later.
Or do I have to say it this way instead:
I forgot about it a few minutes later.
You can. But usually the unadorned phrase minutes later (or seconds later) is reserved for emphasizing shortness of time in a way that "a few minutes later" doesn't really manage to convey, despite the fact that brevity would seem to be underscored by a qualifier like "a few" (which term is more likely to call attention to the inconsequentiality of the fact itself).