Using the calibration function is suggested to increase the accuracy of approximate equations in the lattice-gas model at calculating various concentration dependences of equilibrium characteristics for nonideal adsorption systems in the vicinity of the critical point. This function should provide a shift of the approximate result to the exact one, when the lattice-gas model equations are used in the quality of the interpolation tool between the exact solutions. A comparison of approximate equations with Onsager's exact solution preferrably allows a use of the quasi-chemical approximation as the interpolation procedure and the exact information on the critical point. The modified lattice-gas model takes into account next the molecular properties of the Lennard-Jones fluid: the long-range potential of adsorbate-adsorbate, an excluded volume of the adsorption site, and a contribution of the triple interactions, as well as a softness of the lattice structure. The modified lattice-gas model with the calibration function is used for the phase diagram descriptions for argon adsorption on the homogeneous (111) CdCl2 face (two-dimensional systems) and for methane adsorption in carbon slitlike pores (three-dimensional system) as well as the other equilibrium characteristics of mentioned systems.