The electronic structure of the honeycomb lattice iridates Na ₂IrO₃ and Li₂IrO₃ has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j_eff=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j_eff physics in A₂IrO₃. We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na₂IrO₃ and Li₂IrO₃ can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr₂IrO₄.