The need for a mild, low-cost, green environment that is able to produce exotic properties of output nanostructures is appealing nowadays. Employing these requirements, the copper (Cu)—based oxide nanostructures have been successfully synthesised via one-pot reaction using biocompatible natural polyphenol, tannic acid (TA) as both the reducing agent and stabiliser at 60, 70 and 80 °C. The structural and optical studies disclosed the effect of TA on the surface morphology, phase purity, elemental composition, optical microstrain and optical intrinsic energy of this mixed Cu2O and CuO nanostructures. The optically based method describes the comparative details of the multi-band gap in the presence of more than one element with overlapping spectra from the first-derivative absorbance curve $$\frac{\Delta E}{\Delta A}$$ Δ E Δ A and the exponential absorbance of Urbach tail energy $${E}_{U}$$ E U towards the conventional Tauc bandgap. The $$\frac{\Delta E}{\Delta A}$$ Δ E Δ A demonstrates that the pronounced effect of TA that Cu2O and CuO nanostructures creates much sensitive first-derivative bandgap output compared to the Tauc bandgap. The results also show that the $${E}_{U}$$ E U reduced as the temperature reaches 70 °C and then experienced sudden increase at 80 °C. The change in the pattern is parallel to the trend observed in the Williamson–Hall microstrain and is evident from the variations of the mean crystallite size $${D}_{m}$$ D m which is also a cause response to the change in temperature or pH. Therefore, the current work has elucidated that the structural and optical correlations on the as-synthesised Cu2O and CuO nanostructures in the presence of TA were the combined reaction of pH change and the ligand complexation reactions. The acquired results suggest a more comprehensive range of studies to further understand the extent relationship between the physical and optical properties of TA functionalised Cu-based oxide nanostructures.