This paper develops a Pinch Analysis based understanding of resource allocation networks (RANs) involving forbidden matches. Prior works on Pinch Analysis have ranged from a simple source-sink model to segregated demand zones, from continuous processes to batch processes, etc. However, RANs with forbidden matches are addressed mainly by mathematical optimization approaches. This paper extends the concept of Pinch Analysis to exploit the underlying structure of problems involving forbidden matches and provides some essential physical insights to these problems. A methodology is developed for minimizing resources in problems involving forbidden matches and identifying whether the obtained solution is optimal or not. The proposed methodology solves the overall problem by taking a demand at a time with the unutilized sources left after solving the previous demands. The methodology establishes that the optimality of the solution depends on the final left over sources and the distribution of pinch qualities obtained while solving each demand in a sequential manner. The applicability of the proposed methodology is demonstrated through an illustrative example of carbon constrained energy sector planning.