We study the emission properties of confined polariton states in shallow zero-dimensional traps under nonresonant excitation. We evidence several relaxation regimes. For slightly negative photon-exciton detuning, we observe a nonlinear increase of the emission intensity, characteristic of carrier-carrier scattering assisted relaxation under strong-coupling regime. This demonstrates the efficient relaxation toward a confined state of the system. For slightly positive detuning, we observe the transition from strong to weak coupling regime and then to single-mode lasing.