Motivated by recent interest in perovskite surfaces and heterostructures, we present an analysis of the Kubo conductivity of a two-dimensional electron gas (2DEG) formed in the $t_{2g}$ bands of an oxide with perovskite structure. We find that when the electric field is polarized in the plane of the 2DEG, the optical conductivity is dominated by nearly independent Drude contributions from two-dimensional subband Fermi surfaces, whereas for perpendicular-to-plane polarization it has strong intersubband features. Our analysis suggests that perpendicular-to-plane optical conductivity studies may help advance understanding of the interplay between lattice distortions and electron-electron interactions in complex oxide 2DEG quantum confinement physics.