We present an abundance analysis of seven super star clusters in the disk of M83. The near-infrared spectra of these clusters are dominated by red supergiants, and the spectral similarity in the J-band of such stars at uniform metallicity means that the integrated light from the clusters may be analyzed using the same tools as those applied to single stars. Using data from VLT/KMOS, we estimate metallicities for each cluster in the sample. We find that the abundance gradient in the inner regions of M83 is flat, with a central metallicity of [Z]= 0.21 +/- 0.11 relative to a solar value of Z(circle dot) = 0.014, which is in excellent agreement with the results from an analysis of luminous hot stars in the same regions. Compiling this latest study with our other recent work, we construct a mass-metallicity relation for nearby galaxies based entirely on the analysis of RSGs. We find excellent agreement with the other stellar-based technique-that of blue supergiants-as well as with temperature-sensitive ("auroral" or "direct") H II-region studies. Of all the H II-region strong-line calibrations, those that are empirically calibrated to direct-method studies (N2 and O3N2) provide the most consistent results.