Why do dopamine receptor antagonists result in elevated prolactin levels?

Because dopamine is an important neurotransmitter in suppressing prolactin release through the tuberoinfundibular pathway.

The tuberoinfundibular pathway comprises dopaminergic projections from the arcuate and periventricular nuclei of the hypothalamus to the infundibular region, also in the hypothalamus or median eminence. Dopamine is released into the portal circulation from the median eminence with the anterior pituitary gland. Dopamine tonically inhibits prolactin release via D2-like receptors, D2 and likely to a lesser extend D4.

Thus, dopamine D2 receptors antagonists increase prolactin release. This explains why antipsychotic drugs and antiemetic drugs acting as antagonists at D2 dopamine receptors can cause hyperprolactinaemia.