The ever-increasing false data injection (FDI) attack on the demand side brings great challenges to the energy management of interconnected microgrids. To address those aspects, this article proposes a resilient optimal defensive strategy with the distributed deep reinforcement learning (DRL) approach. To evaluate the FDI attack on demand response (DR), an online evaluation approach with the recursive least-square (RLS) method is proposed to evaluate the extent of supply security or voltage stability of the microgrids system is affected by the FDI attack. On the basis of evaluated security confidence, a distributed actor network learning approach is proposed to deduce optimal network weight, which can generate an optimal defensive scheme to ensure the economic and security issue of the microgrids system. From the methodology's view, it can also enhance the autonomy of each microgrid as well as accelerate DRL efficiency. According to those simulation results, it can reveal that the proposed method can evaluate FDI attack impact well and an improved distributed DRL approach can be a viable and promising way for the optimal defense of microgrids against the FDI attack on the demand side.