DFT calculations of defects in transition-metal oxides constitute a challenging task, often requiring advanced methods to ensure a reasonable description of the electronic structure and large supercells to mimic the dilute defect concentration. Several contradicting DFT results were reported for oxygen vacancies (V_O) in SrTiO₃ (STO) and were often related to the peculiar properties of STO, which is a d⁰ transition metal oxide with mixed ionic-covalent bonding. Here, for the first time, we apply the extended Hubbard DFT+U+V approach, including on-site (Ti-3d) as well as inter-site (Ti-3d and O-2p) electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via density-functional perturbation theory. The negligible additional cost of DFT+U+V compared to standard DFT enables the treatment of large supercells, yet the obtained structural and electronic properties agree well with hybrid-functional calculations and experiments. As such, DFT+U+V results in a bandgap and crystal field splitting for STO in good agreement with experiments. In turn, the description of the electronic properties of V_O is improved, with formation energies much less dependent on the cell size compared to DFT+U and in excellent agreement with experiments.