A systematic analysis of the experimental cross-section data in odd mass number $(A)$ and odd atomic number $(Z)$ nuclei is reported to reveal a novel mass-energy systematics for the pre-compound emission of fast neutrons in $\ensuremath{\alpha}$-induced reactions at low energies. The experimental excitation functions have been analyzed within the framework of statistical model predictions to get information regarding pre-compound emission. The present analysis establishes for first time an interesting systematics, emphasizing that accessible excitation energy on peripheral nucleons of the systems is an exponential function of atomic mass number ($A$) of target nuclei. One of the most important features of this systematics is to provide a precise estimation of the pre-compound contribution for any nuclei, except closed-shell ones, over a wide range of mass number $63\ensuremath{\le}A\ensuremath{\le}109$ in the nuclear landscape. New results of the present analysis emphasize an additional subtle interconnection between the structure of nuclei and the nuclear reaction mechanism of the pre-compound emission process at low energies, where the compound nucleus process is more likely to be dominant.