This paper considers a two-tier femto-macro overlay network architecture, where groups of femtocells are overlaid by macrocells. The capacity of the femtocells is limited, thus redirection of blocked femto calls to the overlaid macrocell is used as a QoS assurance strategy. Similar overflow approaches have been used in telephony; however, extension of this approach to capacity-constrained femto-macro overlay networks poses significant challenges due to the wide variety of bandwidth requirement of Internet services, the large number of femtocells overlaid by a macrocell, and the need for fast computations imposed by practical requirements of dynamic real-time resource allocation. We propose a new computationally efficient numerical method for the loss probability approximation in such two-tier femto-macro overlay networks. The accuracy of the method is verified by exact Markov-chain solutions for small systems and by simulations for larger systems.