We demonstrate how to tailor the losses of nonlinear cavities in order to suppress their reflection and enhance their nonreciprocal transmission. We derive analytical expressions predicting the existence of zero-reflection channels in single and coupled nonlinear cavities, depending on the driving frequency and loss rates. While suppressing the reflection from a single cavity imposes a stringent condition on the input-output leakage rates, we demonstrate that this condition can be significantly relaxed in systems of coupled cavities. In particular, zero-reflection and nonreciprocity can be achieved across a range of driving frequencies in coupled cavities by tuning the output leakage rate alone. Numerical calculations based on the driven-dissipative Gross-Pitaevskii equation, usually employed to describe microcavity polaritons, reveal the spatial phenomenology associated with zero-reflection states and provide design guidelines for the construction of nonlinear optical isolators.