We report on the design, optimization and fabrication of a plasmon-assisted terahertz (THz) photoconductive antenna (PCA) for THz pulse generation at low-power optical pumps. The PCA features a high aspect ratio dielectric-embedded plasmonic Au grating placed into the photoconductive gap. Additionally, Si3N4-passivation of the photoconductor and the Al2O3-antireflection coating are used to further enhance antenna performance. For comparative analysis of the THz photocurrents, THz waveforms and THz power spectra we introduced the THz photocurrent δi and the THz power enhancement δTHz factors, which are defined as ratios between the THz photocurrents and the THz power spectra for the plasmon-assisted and conventional PCAs. We demonstrated superior performance of the plasmon-assisted PCA δi=30 and δTHz=3 ⋅ 103 at the lowest optical pump power of P=0.1 mW. Nevertheless the increase to P=10 mW lead to monotonically decrease in the both values to δi=2 and δTHz=102 due to screening effects. These results demonstrate a strong potential of the plasmonic PCA for operation with low-power lasers, thus, opening opportunities for the development of portable and cost-effective THz spectrometers and imaging systems.