Recent studies reveal a potential compensating effect between cloud response to warming and to aerosol in climate models. However, it remains undetermined whether such relationship is driven by common physical processes, by their dependency on the climate state, or the combination of both. Here we show a robust anti-correlation between the normalized cloud feedback (defined as the fractional change of cloud radiative effect due to surface warming) and normalized effective radiative forcing due to aerosol-cloud interactions (ERFaci) from an E3SMv2 perturbed parameter ensemble. The decomposition analysis using a radiation kernel indicates that the relationship is primarily dominated by the shortwave radiation responses related to cloud optical depth change in non-low clouds. The anti-correlation is attributed largely to their dependency on the unperturbed mean-state climate. We also quantify the difference in the correlations between the normalized cloud feedback and ERFaci due to microphysics, turbulence, and deep convection. This study provides a process-level understanding of the relationship between cloud feedback and aerosol-cloud interaction and provides insights into how to simultaneously constrain the two major sources of uncertainty in climate modeling.