Oxygen vacancies are a common source of excess electrons in complex oxides. In Mott insulators, these additional electrons can induce a metal-insulator transition (MIT), fundamentally altering the electronic properties of the system. Here we study the effect of oxygen vacancies in LaTiO3, a prototypical Mott insulator close to the MIT. We show that the introduction of oxygen vacancies creates a vacancy-related band immediately below the partially filled Ti-t 2g bands. We study the effect of this additional band on the Mott MIT using a combination of density functional theory and dynamical mean-field theory (DFT+DMFT), employing a minimal correlated subspace consisting of effective Ti-t 2g orbitals plus an additional Wannier function centered on the vacancy site. We find that the Mott insulating state in LaTiO3 is robust to the presence of the vacancy band, which remains fully occupied even in the presence of a local Coulomb repulsion, and therefore does not cause a doping of the Mott insulator