The increase in the production and consumption of pharmaceuticals increases their presence in the global environment, which may result in direct threats to living organisms. For this reason, there is a need for new methods to analyze drugs in environmental samples. Here, a new procedure for separating and determining selected drugs (diclofenac, ibuprofen, and carbamazepine) from bottom sediment and water samples was developed. Drugs were determined by ultra-high performance liquid chromatography coupled with an ultraviolet detector (UHPLC-UV). In this work, a universal and single-step sample treatment, based on supramolecular solvents (SUPRAS), was proposed to isolate selected anticonvulsants and nonsteroidal anti-inflammatory drugs (NSAIDs) from sediment samples. The following parameters were experimentally selected: composition of the supramolecular solvent (composition THF:H2O (v/v), amount of decanoic acid), volume of extractant, sample mass, extraction time, centrifugation time, and centrifugation speed. Finally, the developed procedure was validated. A Speedisk procedure was also developed to extract selected drugs from water samples. The recovery of analytes using the SUPRAS procedure was in the range of 88.8–115%, while the recoveries of the Speedisk solid-phase extraction procedure ranged from 81.0–106%. The effectiveness of the sorption of the tested drugs by sediment was also examined.