Cell behavior is mediated by variety of physiochemical properties of the extracellular matrix (ECM). Mechanical stiffness of ECM, in particular, is found to be a major regulator for the multiple aspects of cellular function. Experiments show that cells generally exhibit an apparent adhesion preference for stiffer substrates. The effect of substrate elasticity is also found to be strongly coupled with adhesivity of the substrate. To understand the underlying physics of rigidity sensing mechanism in cells, in this study we use a vesicle-substrate system to model cell adhesion as a first order approximation. Within this framework, an equilibrium thermodynamic analysis is undertaken to elucidate the interplay between substrate compliance and equilibrium configuration of an adherent vesicle. The equilibrium adhesion is assumed to ensure minimization of the free energy contributed by substrate deformation and interfacial adhesive and repulsive interactions between the membrane and substrate. The predictions of this purely mechanistic model are found to be qualitatively analogous to some of the characteristic features of cell adhesion to compliant bio-adhesive substrates. This observation suggests that the physical aspects of the membrane-substrate interfacial interactions could passively contribute in regulation of the rigidity sensing by cells.