In this paper we generalize the potential inequality which was introduced in [6] and extended to the class of naturally defined convex functions in [1]. The generalization is achieved by replacing the 1st order Taylor expansion of a convex function in the proof of the potential inequality with the n-th order Taylor expansion of an (n + 1)-convex function. Furthermore, by using methods developed in [4] and [2] we construct several families of n-exponentially convex functions by making use of linearity of the generalized potential inequality.