A series of high-pressure methane adsorption measurements were performed at various temperatures on whole shale and kerogen samples collected from the Lower Longmaxi shale in the Nanchuan area, southeast Sichuan Basin, to investigate supercritical methane adsorption properties and evaluate in-place methane storage capacity as a function of burial depth. The results show that the supercritical Dubinin–Radushkevich (SDR) model fits the excess adsorption isotherms marginally better than the supercritical Langmuir model. However, the fitted adsorbed methane density of kerogens obtained from the SDR model may be greater than the liquid methane density at the atmospheric boiling point (0.423 g/cm3). The proposed multiple regression fitting carried out in this work illustrates that approximately 57.59% (34.51–85.45%) and 37.60% (10.74–59.52%) of the methane adsorption capacity at 333.15 K can be attributed to organic matter (OM) and clay minerals (CMs), respectively, for whole shales investigated. According to thermodynamic analyses, the significant contribution of OM to the methane adsorption capacity can be attributed to the stronger affinity between kerogens and methane molecules in contrast to that between CMs and whole shales. The methane storage capacity estimated as a function of burial depth showed that the adsorbed gas storage capacity declines with increasing burial depth between 2000 and 5000 m, while the free gas storage capacity shows the opposite trends. Gas accumulation pressure primarily exerts a significant effect on the free gas storage capacity rather than adsorbed gas storage capacity, and adsorbed gas storage capacity begins to exceed free gas storage capacity at shallow burial depths for normally pressured gas accumulations. Normally pressured shale gas accumulations at shallow burial depths, which are widely distributed in the residual syncline of the study area, should be given more attention due to their relatively low development costs and relatively high storage capacity for adsorbed gas.