The presence of defects, such as copper and oxygen vacancies, in cuprous oxide films determines their characteristic carrier conductivity and consequently their application as semiconducting systems. There are still open questions on the induced electronic re-distribution, including the formation of polarons. Indeed, to accurately reproduce the structural and electronic properties at the cuprous oxide surface, very large slab models and theoretical approaches that go beyond the standard generalized gradient corrected density functional theory are needed. In this work we investigate oxygen vacancies formed in proximity of a reconstructed Cu₂O(111) surface, where the outermost unsaturated copper atoms are removed, thus forming non-stoichiometric surface layers with copper vacancies. We address simultaneously surface and bulk properties by modelling a thick and symmetric slab, to find that hybrid exchange-correlation functionals are needed to describe the oxygen vacancy in this system. Our simulations show that the formation of oxygen vacancies is favoured in the sub-surface layer. Moreover, the oxygen vacancy leads to a splitting and left-shift of the shallow hole states in the gap, which are associated with the deficiency of copper at the surface. These findings suggest that surface electronic structure and reactivity are sensitive to the presence of oxygen vacancies, also when the latter are formed deeper within the film.