One of the key phenomena that determine the fluorescence of nanocrystals is the nonradiative Auger-Meitner recombination of excitons. This nonradiative rate affects the nanocrystals' fluorescence intensity, excited state lifetime, and quantum yield. Whereas most of the above properties can be directly measured, the quantum yield is the most difficult to assess. Here we place semiconductor nanocrystals inside a tunable plasmonic nanocavity with subwavelength spacing and modulate their radiative de-excitation rate by changing the cavity size. This allows us to determine absolute values of their fluorescence quantum yield under specific excitation conditions. Moreover, as expected considering the enhanced Auger-Meitner rate for higher multiple excited states, increasing the excitation rate reduces the quantum yield of the nanocrystals.