The recent development of the Internet of Things (IoT) devices offers an intelligent concept for integrating massive number of interconnected wireless devices. However, supporting such massive number of IoT connections (hundreds of billions) requires an efficient and dynamic spectrum access strategy. Accordingly, the integration of non‐orthogonal multiple access (NOMA) in the cognitive radio (CR) systems, referred to as a multi‐carrier NOMA CR‐enabled system, is envisioned as a potential spectrum‐efficient networking paradigm that can support massive energy‐efficient IoT connectivity in B5G networks while maintaining the quality of services (QoS) of the IoT devices. However, the power consumption issue of the multi‐carrier NOMA CR‐based system becomes as one of key challenges, especially when considering the expected massive connectivity. Accordingly, several power‐aware optimization frameworks have been considered to address this issue. While most of the existing CR‐based multi‐carrier NOMA power allocation mechanisms only optimize the allocated per‐user power, this article proposes a novel joint bandwidth and power allocation problem over each available idle channel with the aim of minimizing the overall transmission power under a set of QoS constrains. Specifically, the bandwidth of each channel is adaptively subdivided into two variable‐width sub‐channels, each is capable to serve a group of CR users using power‐domain NOMA. This novel design is formulated as a joint optimization problem that is shown to be a non‐convex. Therefore, an iterative algorithm with a second‐order cone programming is deployed to handle the non‐convexity of the problem, and thus, determine the solution of it. Simulation results reveal that the developed variable bandwidth adaptive power allocation mechanism outperforms the conventional equal sub‐channel allocation in terms of the required transmission power, which significantly improves the energy efficiency in the system.