We study ultracold dipolar excitons confined in a 10 μm trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons. Specifically, in this regime and below a critical temperature of about 1 K, we show that for a local density n∼(2-3)×10^{10} cm^{-2} a coherent quasicondensate phase forms in the inner region of the trap, encircled by a more dilute and normal component in the outer rim. Remarkably, this spatial arrangement correlates directly with the concentration of defects in the exciton density, which is strongly decreased in the quasicondensed region, consistent with a superfluid phase. Thus, our observations point towards a Berezinskii-Kosterlitz-Thouless crossover for two-dimensional excitons.