The Moon bears a striking compositional and isotopic resemblance to the bulk silicate Earth (BSE) for many elements, but is considered highly depleted in many volatile elements compared to BSE due to high-temperature volatile loss from Moon-forming materials in the Moon-forming giant impact and/or due to evaporative loss during subsequent magmatism on the Moon. Here, we use high-pressure metal-silicate partitioning experiments to show that the observed low concentrations of volatile elements sulfur (S), selenium (Se), tellurium (Te), and antimony (Sb) in the silicate Moon can instead reflect core-mantle equilibration in a largely to fully molten Moon. When incorporating the core as a reservoir for these elements, their bulk Moon concentrations are similar to those in the present-day bulk silicate Earth. This suggests that Moon formation was not accompanied by major loss of S, Se, Te, Sb from Moon-forming materials, consistent with recent indications from lunar carbon and S isotopic compositions of primitive lunar materials. This is in marked contrast with the losses of other volatile elements (e.g., K, Zn) during the Moon-forming event. This discrepancy may be related to distinctly different cosmochemical behavior of S, Se, Te and Sb within the proto-lunar disk, which is as of yet virtually unconstrained.