Energy storages (ESs) have been widely utilized in DC microgrids to regulate power surplus/deficit cooperatively, such that renewable energy sources can be liberated to capture maximum energy independently. However, minimizing the operation loss of DC microgrids by ESs while ensuring nominal system voltage and ES safety is the desired control objective that needs further exploration. This paper formulates the desired control objective as a non-smooth convex optimization problem and designs a distributed optimal controller for ESs to achieve this objective. To bridge the gap between the optimization problem and controller design, an optimality condition, which is more unified and concise than the traditional KKT condition, is proposed based on the projection operation. Additionally, considering unavoidable time delays in communication systems, the adverse effect of communication delays on the proposed controller is analyzed from a novel perspective of disturbance injection. Furthermore, a robust control strategy is proposed to eliminate the adverse effect of communication delays by imitating the feedback control model from the Lagrange dual problem. Numerical simulations on a detailed switch-level model demonstrate the stability, optimality, robustness, resilience, and scalability of the proposed distributed optimal controller in minimizing the operation loss of DC microgrids.