In recent times, the multi-valued logic (MVL) design has been widely explored in the designing of digital computing circuits as the goals of enhanced processing capability with reduced interconnect complexity and small chip area are achieved. Hence, this work describes the design methodology of ternary logic-based asynchronous and synchronous up-counter, down-counter, and ring-counter designs using D-flip-flops in carbon nanotube technology. Carbon nanotube-field-effect transistors (CNTFETs)’ unique feature of altering the device threshold voltage by making variations in CNT diameter is exploited for the realization of multiple voltages in ternary logic design. Here the principle of the master-slave scheme is adopted for the designing of Dual shift-single shift and Single shift-dual shift-D-flip-flop circuits using the cyclic property of shifting operators. These flip-flop designs are further extended to construct multiple-digit counter structures which are suitable for realizing the logic functionality of up-counter, down-counter, and ring-counter designs. To exploit ternary logic increased computation capability benefit, a mode control up/down counter circuit is designed in which a single module is generating up and down-counting sequence based on applied mode input. To investigate the performance of the proposed designs, the simulations are performed using the Synopsys HSPICE simulator considering the 32 nm Stanford CNTFET model. According to the simulation results, a maximum energy consumption reduction up to 55% is obtained compared to the counterpart. Hence, the increased computational capability of three-valued logic is exploited in the presented work to achieve energy enhancements in designing ternary sequential circuits.