This paper outlines a procedure for loss allocation in both radial and meshed distribution networks with distributed generation that could be regulated in various ways. The method is analytically developed based on the theory of electrical circuits combined with game theory based on Aumann-Shapley, which guarantees both the electrical principles and the fair axioms of game theory. The proposed method obtains unitary participation coefficients for each network user based on the currents demanded/injected by each user and the network topology. The proposed allocation method based on Aumann-Shapley has been compared with other traditional allocation methods, is adaptable to distribution networks, and shows great potential and ease of implementation. Moreover, it can be applied to any kind of distribution network (radial or meshed) with distributed energy resources.