To me it made perfect sense that they could make those tiny bite wounds and then drink from them without spilling.
A)They already have all kind of weird tricks and aren't human anyway, so being a tidy eater wasn't really a stretch. If anything it made them creepier.
B)Vamps are nobles, rich folk and stuff. Those people learn to eat without making a mess. It's in their blood.
Plus vampires drinking from (wine) glasses (or bottles)- without straws -was a thing in at least a few stories.
*Outside of cases where they explicitely feed in more exotic ways I mean. But I don't think I read (many of) those as a kid.