We perform a combined experimental and theoretical study of tetramethyltetraselenafulvalene (TMTSF) single-crystal field-effect transistors, whose electrical characteristics exhibit clear signatures of the intrinsic transport properties of the material. We present a simple, well-defined model based on physical parameters and we successfully reproduce quantitatively the device properties as a function of temperature and carrier density. The analysis allows its internal consistency to be checked, and enables the reliable extraction of the density and characteristic energy of shallow and deep traps in the material. Our findings provide indications as to the origin of shallow traps in TMTSF transistors.