We experimentally investigate how disorder comes about in parametrically excited waves on a fluid surface (Faraday waves). We find that the transition from an ordered pattern to disorder corresponding to "defect-mediated turbulence" is mediated by a spatially incoherent oscillatory phase. This phase consists of highly damped waves that propagate through the effectively elastic lattice defined by the pattern. They have a well-defined frequency, velocity, and transverse polarization. As these waves decay within a few lattice spaces, they are spatially and temporally uncorrelated at larger scales.