Performance of control systems interacting over a shared communication network is tightly coupled with how the network provides services and distributes resources. Novel networking technology such as 5G is capable of providing tailored services for a variety of network demands. Stringent control requirements and their critical performance specification call for online adaptable and control-aware network services. This perspective suggests a co-design of physical and network layers aiming to ensure that the necessary quality-of-service is provided to achieve the desired quality-of-control. An optimal co-design is in general challenging due to cross-layer couplings between the physical and network layers and their layer-specific functionalities. Furthermore, the complexity of the co-design depends on the level of actionable information the layers share with each other. In this Part I of a two-letter series, we present a general co-design of physical operations and service allocation aiming to minimize a social regret measure for networked control systems. We introduce an optimal networked co-design scenario using the regret index as the joint quality-of-control and quality-of-service (QoC-QoS) measure, and discuss the role of cross-layer awareness in the structure of optimization problems. We mainly focus on the finite-horizon case but we briefly present the infinite-horizon case as well. In Part II, we discuss regret-optimal cross-layer policies for Gauss-Markov systems and derive the optimal solutions based on the general problems introduced in Part I.