The influence of non-equilibrium carrier dynamics on pulse propagation through inverted semiconductor gain media is investigated. For this purpose, a fully microscopic many-body model is coupled to a Maxwell solver, allowing for a self-consistent investigation of the light-matter-coupling and carrier dynamics, the optical response of the laser and absorber in the multiple-quantum-well medium, and the modification of the light field through the resulting optical polarization. The influence of the intra-pulse dynamics on the magnitude and spectral dependence of pulse amplification for single pulses passing through inverted quantum-well media is identified. In this connection, the pulse-induced non-equilibrium deviations of the carrier distributions, the kinetic-hole filling kinetics in the gain medium, and the saturable-absorber-relaxation dynamics are scrutinized. While pulses shorter than about 100 fs are found to be rather unaffected by the carrier-relaxation dynamics, the pump-related dynamics become prominent for pulses in the multi-picosecond range leading to significant amplification.