The solution to the well-known loss allocation problems in interconnected power networks has usually been through power-flow analysis. This power-flow based approach is computationally intensive and the results may not converge for large practical power systems. This paper, therefore, explores an alternative approach to solving this problem using the Inherent Structural Characteristics Theory (ISCT) [6]. The total transmission loss within power network based on both the ISCT and power-flow-based approach is determined, and then used to allocate losses to loads in the network. The results obtained from the two approaches are compared. The ISCT approach, apart from being faster, allocates the total loss within the network to loads in a fairer, equitable and transparent manner. Matlab 2013a is employed as a simulation tool. The sparsity inherent in power networks is explored to reduce the computational intensity and computer memory required. This new approach is tested on a standard IEEE 14-bus system and a practical system of the Nigerian 40-bus network. The results obtained from the simulations show the ISCT approach to be superior.