Demand response (DR), where electricity consumption is shifted in response to incentive signals, can ease the transition to renewable generation. However, when many devices simultaneously respond to these signals there is the potential for violating local network constraints. Many of the proposed solutions require consumers to hand over control of their devices to third-parties. Here, we propose a method of using price distortions to coordinate distributed resources, which is both robust to local constraints and privacy preserving. We formulate the price distortion setting problem as a mixed-integer linear programming problem. Conditions are derived under which the method can guarantee constraint violations are eliminated within one time step. The method was tested using case studies involving both electric vehicles and smart heating/cooling systems. We show that the proposed method, under a scenario with maximum DR participation, can achieve 98% of the theoretical lower bound on the number of constraint violations. Furthermore, our method out-performs the benchmark where some devices opt-out of DR.