We show that dissipative coupling between an array of passive optical resonators creates a ladder of decay rates in the complex eigenfrequencies. This effect promotes mode discrimination in laser arrays, while the lowest-order and highest-order modes exhibit the highest and lowest lasing thresholds, respectively. The array supermodes and their corresponding eigenfrequencies are calculated analytically through a tight-binding model, and the single-mode operation range is derived. The results are exemplified through the finite element simulation of an array of transversely coupled semiconductor laser cavities.