This study reveals the error analysis of Hermite-Hadamard inequality for coordinated convexity related to post-quantum integrals. At first, we establish a multi-parameter identity pertaining coordinated convexity via post-quantum integrals followed by new integrals to construct our main results. By utilizing this generic identity, we analyze the error estimates of classical Hermite-Hadamard inequality in the post-quantum context. Application of power mean inequality enables the refinement of bounds involved and extends it further. We make use of graphical representation with the help of concrete examples to verify the validity of presented results. In the end, to focus on usability and significance of the results, two applications through polynomial functions are produced.