We measure the magnetocaloric effect of the manganite series La0.67Ca0.33-xSrxMnO3 by determining the isothermal entropy change upon magnetization, using variable-field calorimetry. The results demonstrate that the field dependence of the magnetocaloric effect close to the critical temperature is not given uniquely by the critical exponents of the ferromagnetic-paramagnetic phase transition, i.e., the scaling is nonuniversal. A theoretical description based on the Bean-Rodbell model and taking into account compositional inhomogeneities is shown to be able to account for the observed field dependence. In this way the determination of the nonuniversal field dependence of the magnetocaloric effect close to a phase transition can be used as a method to gain insight into the strength of the spin-lattice interactions of magnetic materials. The approach is shown also to be applicable to first-order transitions.