A simple procedure leading to disposable potentiometric sensors using as a supporting electrode - electrical lead and transducer - a layer of carbon nanostructured material, either graphene or multi-walled nanotubes, is proposed, and the effect of the material used on the properties of the sensor is discussed. The obtained layers were partially covered with a conventional poly(vinyl chloride) (PVC) based ion-selective membrane to result in simple, planar, and disposable potentiometric sensors. The analytical performance of the thus obtained electrodes was compared with that of classical macroscopic all-solid-state ion-selective electrodes (e.g. employing poly(octylthiophene) as a solid contact and a similar ion-selective membrane). It was superior (taking into account detection limits or selectivity towards Na(+) ions) compared to that of other disposable sensors proposed recently. The observed excellent analytical performance was attributed to the applied method of preparation of carbon nanostructured materials, which does not require addition of a surfactant to obtain a stable suspension (ink) used to prepare the electrical lead and the transducer of the sensor. Although the proposed sensors are predominantly intended for disposable use, pronounced stability of potential readings was obtained in within-day experiments. Moreover, due to their high conductivity carbon-plastic electrodes can be also applied in polarized potentiometric measurements.