© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Ternary solvent extraction investigated as green technology to obtain anthocyanin-rich extracts from black carrots. A central composite design was used to optimize the extraction pressure (100–400 bar), extraction temperature (20–60 °C), and ethanol/water ratio (10/90–90/10). The extraction time (40 min) and the flow rate of CO2 (50 g/min) and the flow rate of ethanol–water mixture (10 mL/min) was kept constant. Response surface methodology was employed for optimization and 3D response surfaces were depicted using the mathematical model. All the trials were found to be at two-phase region according phase equilibrium diagram of for CO2–ethanol–water mixtures. The linear and quadratic effect of pressure and temperature were found to be significant (p < 0.05), however, only the quadratic effect of ethanol–water ratio was found to be significant (p < 0.05). The optimized process parameters were estimated to be pressure of 304 bar, temperature of 52 °C, ethanol/water ratio of 48/52. Extraction using these optimum parameters gave the best total monomeric anthocyanin content (123 mg/L), total phenolic content (62 mg/100 mL), total flavonoid content (44 mg/100 mL), CUPRAC (473 mg/100 mL) and DPPH (120 mg/100 mL) antioxidant capacity. The experimental values were coherent with those predicted, thus expressing the fitness of the model and the success of CCD in the optimization of extraction conditions. Conventional extraction was also applied, and it was found that higher extraction efficiencies are possible with pressurized extraction. Graphical abstract: [Figure not available: see fulltext.].