In the present work, we demonstrate a facile and single-step hydrothermal synthesis of chalcopyrite based carbon composite material (CuFeS2/carbon nanotubes) with the unique architecture in which the porous CuFeS2 (CFS) microflowers are encapsulated by the carbon nanotubes (CNT). The structural, morphological, compositional, chemical, vibrational and electrochemical properties of the fabricated CFS/CNT composite are analyzed in detail through comprehensive characterization techniques. When used as binder-free negative electrode material in the supercapacitor application, the CFS/CNT composite exhibits exceptional electrochemical performance than its pristine form (CFS). The electrochemical analysis clearly reveals the pseudocapacitive nature of composite electrode with improved electrical and charge-transport properties. In three-electrode configuration, the CFS/CNT composite electrode exhibits a high specific capacitance of 667F/g, a high columbic efficiency of 95% with 100% cyclic stability for 3000 cycles. The key factors influencing the supercapacitive performance of the electrodes are validated using extensive experimental results and are backed up with theoretical calculations of the relevant simulated models. The plausible storage sites of Na+ ions along with its valence charge transfer, electronic properties and binding characteristics on the composite electrode are identified through first-principles density functional theory (DFT) calculations. Furthermore, to evaluate its feasibility for practical application, a solid-state symmetric device (CFS/CNT//CFS/CNT) based on polymer gel electrolyte (PVA-Na2SO4) was fabricated. The symmetric device exhibited the highest specific capacitance of 128F/g, an energy density of 22 Wh/kg, a power density of 2083 W/kg and notable durability (94% cyclic stability for 10,000 cycles) reflecting its formidable candidature for future energy storage systems.