The two-dimensional electron gas at the LaTiO3/SrTiO3 or LaAlO3/SrTiO3 oxide interfaces becomes superconducting when the carrier density is tuned by gating. The measured resistance and superfluid density reveal an inhomogeneous superconductivity resulting from percolation of filamentary structures of superconducting "puddles" with randomly distributed critical temperatures, embedded in a nonsuperconducting matrix. Following the evidence that superconductivity is related to the appearance of high-mobility carriers, we model intrapuddle superconductivity by a multiband system within a weak coupling BCS scheme. The microscopic parameters, extracted by fitting the transport data with a percolative model, yield a consistent description of the dependence of the average intrapuddle critical temperature and superfluid density on the carrier density. © 2013 American Physical Society.