We investigated the nematic to smectic transition undergone by parallel hard spherocylinders in the framework provided by the residual multiparticle entropy (RMPE) formalism. The RMPE is defined as the sum of all contributions to the configurational entropy of the fluid that arise from density correlations involving more than two particles. The vanishing of the RMPE signals the structural changes that take place in the system for increasing pressures. Monte Carlo simulations carried out for parallel hard spherocylinders show that such a one-phase ordering criterion accurately predicts also the nematic-smectic transition threshold notwithstanding the almost continuous character of the transition. A similar quantitative correspondence had been already noted in the case of an isotropic fluid of freely rotating hard spherocylinders undergoing a transition to a nematic, smectic, or solid phase. The present analysis confirms the flexibility of the RMPE approach as a practical and reliable tool for detecting, the formation of mesophases in model liquid crystals.