Optical losses in metals represent the largest limitation to the external quantum yield of emitters coupled to plasmonic antennas. These losses can be at the emission wavelength, but they can be more important at shorter wavelengths, i.e., at the excitation wavelength of the emitters, where the conductivity of metals is usually lower. We present accurate measurements of the absolute external photoluminescent quantum yield of a thin layer of emitting material deposited over a periodic nanoantenna phased array. Emission and absorptance measurements of the sample are performed using a custom-made setup including an integrating sphere and variable angle excitation. The measurements reveal a strong dependence of the external quantum yield on the angle at which the optical field excites the sample. Such behavior is attributed to the coupling between far-field illumination and near-field excitation mediated by the collective resonances supported by the array. Numerical simulations confirm that the inherent losses associated with the metal can be greatly reduced by selecting an optimum angle of illumination, which boosts the light conversion efficiency in the emitting layer. This combined experimental and numerical characterization of the emission from plasmonic arrays reveals the need to carefully design the illumination to achieve the maximum external quantum yield.