For heavy meson systems, we study the heavy quark potential, which emerges from the effective dilaton-gluoncoupling inspired from the superstring theory. We put emphasis on the new confinement generating mechanism of thispotential through the investigation of the spin-averaged energy levels of the heavy meson systems. By using a unifiedapproach to the solutions of the Schrodinger and the spinless Salpeter equations, we can examine in a realistic waythe effects of using a relativistic kinetic energy. The obtained results agree favourably with other predictions, and therelativistic equation can better account for the observed energy levels.