Transducers made from graphene-type materials are widely used in sensing applications. However, utilization of graphene oxide obtained from electrochemical exfoliation of graphite (EGO) has remained relatively unexplored. In this study, electrochemical cocaine aptasensors based on large-size EGO flakes were investigated. In particular, the influence of the following parameters on the sensor performance was examined: (i) aptamer’s terminal group (−NH2 vs −OH), (ii) functionalization of EGO with the aptamer via physical adsorption and covalent immobilization, and (iii) intrinsic electrochemical properties of EGO such as the electrochemical surface area (ESA) and standard rate constant of electron transfer (k0). The results demonstrate that EGO-based electrochemical aptasensors fabricated by physical adsorption with an NH2-modified aptamer have very good reproducibility, shelf-life stability, and high sensitivity for detecting cocaine with a detection limit of 50 nM. Their performance is comparable to that of the aptasensors prepared using the covalent immobilization. Additionally, it is shown that EGO materials with high ESA and k0 can enhance the sensing performance. The fast (less than 10 min) and strong adsorption of the NH2-modified cocaine aptamer on the surface of large EGO flakes makes the fabrication of the sensing platform simple and rapid. This simple approach has the potential to simplify the fabrication of sensors.