The nabla fractional-order uncertain difference equation with Caputo-type was analyzed in this article. To begin, the existence and uniqueness theorem of solutions for nabla Caputo uncertain difference equations with almost surely bounded uncertain variables was presented. Furthermore, the uncertainty distributions of the solutions for the proposed equations were obtained by establishing a connection between the solutions of equations and their $\alpha$-paths based on new comparison theorems. Finally, an application of the uncertain difference equations in a logistic population model involving Allee effect was provided and examples were performed to demonstrate the validity of the theoretical results presented.