We report on generation of coherent terahertz radiation by photomixing with a photoconductive antenna placed in a three-dimensional photonic crystal cavity. We observed efficiency peaks around the frequencies near the photonic bandedges and at the planar defect modes. The efficiency peaks observed near the photonic bandedges are associated with the increase of the optical mode density at the bandedge. The relatively low efficiency at the planar defect mode frequencies are explained by the mode diffusion in the lateral direction of the defect layer.