Emerging microservices demand flexible low-latency processing of network functions in virtualized environments, e.g., as containerized network functions (CNFs). While ensuring highly responsive low-latency CNF processing, the computing environments should conserve energy to reduce costs. In this systems integration study, we develop and evaluate the novel XDP-Monitoring Energy-Adaptive Network Functions (X-MAN) framework for managing the CPU operational states (P-states) so as to reduce the power consumption while prioritizing low-latency service. Architecturally, X-MAN consists of lightweight traffic monitors that are attached to the virtual network interfaces in the kernel space for per-CNF traffic monitoring and a power manager in user space with a global view of the CNFs on a CPU core. Algorithmically, X-MAN monitors the CPU core utilization via hybrid simple and weighted moving average prediction fed by the traffic monitors and a power management based on step-based CPU core frequency (P-state) adjustments. We evaluate X-MAN through extensive measurements in a real physical testbed operating at up to 10 Gbps. We find that X-MAN incurs significantly shorter and more consistent monitoring latencies for the CPU utilization than a state-of-the-art CPU hardware counter approach. Also, X-MAN achieves more responsive CPU core frequency adjustments and more pronounced reductions of the CPU power consumption than a state-of-the-art code instrumentation approach. We make the X-MAN source code publicly available.