When a person drinks only one or two beers, then stops drinking, the person will inevitably become tired/drowsie. This phrase describes that phenomenon.
Since I've had lunch I've got the onebeer drowsies, should have drank three or four, at least then I'd be able to stay awake.
The complete and utterstate where you have the tendency to accidentaly drop everything you pick up, causing frustration and embarrasment if there are others in the vicinity