A theoretical investigation on slow light propagation based on electromagnetically induced transparency in a three-level quantum-dot system is performed including non-Markovian effects and correlated dephasing reservoirs. It is demonstrated that the non-Markovian nature of the process is quite essential even for conventional dephasing typical of quantum dots leading to significant enhancement or inhibition of the group velocity slow-down factor as well as to the shifting and distortion of the transmission window. Furthermore, the correlation between dephasing reservoirs may also either enhance or inhibit non-Markovian effects.