Human studies have demonstrated the multiple health benefits of fruits and vegetables. Due to its high fiber, mineral and antioxidant content, carrot is an ideal source for the development of nutraceuticals or functional ingredients. Current research assesses accelerated solvent extraction (ASE) traits which affect the antioxidant qualities of carrot extract using response surface methodology (RSM), hierarchical cluster analysis (HCA), and the sum of ranking differences (SRD). A mixture of organic solvents, acetone, and ethanol with or without the addition of 20% water was applied. The total carotenoid and polyphenol contents in extracts, as well as their scavenging activity and reducing power, were used as responses for the optimization of ASE extraction. RSM optimization, in the case of 20% water involvement, included 49% of acetone and 31% of ethanol (Opt1), while in the case of pure organic solvents, pure ethanol was the best choice (Opt2). The results of HCA clearly pointed out significant differences between the properties of extracts with or without water. SRD analysis confirmed ethanol to be optimal as well. RSM, HCA, and SRD analysis confirmed the same conclusion—water in the solvent mixture can significantly affect the extraction efficacy, and the optimal solvent for extracting antioxidants from carrot by ASE is pure ethanol.