In this paper we extend the work synthetically presented by M. Baldicchi, A. V. Nesterenko, G. M. Prosperi, D. V. Shirkov, and C. Simolo [Phys. Rev. Lett. 99, 242001 (2007)] and give theoretical details and a complete set of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an experimental strong coupling ${\ensuremath{\alpha}}_{\mathrm{s}}^{\mathrm{exp}}({Q}^{2})$ below 1 GeV by comparison with the meson spectrum. The BS potential follows from a proper ansatz on the Wilson loop to encode confinement and is the sum of a one-gluon-exchange term and a confinement term. Besides, the common perturbative strong running coupling is replaced by the ghost-free expression ${\ensuremath{\alpha}}_{\mathrm{E}}({Q}^{2})$ according to the prescription of analytic perturbation theory (APT). The agreement of ${\ensuremath{\alpha}}_{\mathrm{s}}^{\mathrm{exp}}({Q}^{2})$ with the APT coupling ${\ensuremath{\alpha}}_{\mathrm{E}}({Q}^{2})$ turns out to be reasonably good from 1 GeV down to 200 MeV, thus confirming quantitatively the validity of the APT prescription in this range. Below this scale, the experimental points could give a hint on the vanishing of ${\ensuremath{\alpha}}_{\mathrm{s}}({Q}^{2})$ as ${Q}^{2}$ approaches zero. This infrared behavior would be consistent with some lattice results as well as with the massive modification of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides quite satisfactory correlated understanding of very high and rather low energy phenomena from a few hundred MeV to a few hundred GeV.