“When had it happened that arterial blood was not enough, and he must rip out the heart and suck it dry also? When had it started that he had to lick the most vicious wounds for the little juice they would yield? He could exist without this, yet he couldn’t resist it, and so he sought—or so he told himself—to make the very most of it when he feasted.” –Prince Lestat, Marius and the Flowers.
Ricean vampires do cry blood tears in the books. Other vampires might not. Claudia would have cried blood tears.
In this production still from a cut scene, it looks like Claudia does have blood tears:
I don’t know why they didn’t actually do it throughout the movie. Looks like they at least tried, though :-
Here’s another production still. Maybe the director didn’t like the thickness of them? Or the fact that they would be difficult to add in physically, since you’d have to redo her makeup for each take? In the books, blood tears are basically regular tears tinged with blood, so they would probably look pink, not so thick and red as these are. These look like ketchup.
I-want-my-IWTV 