Neurocognitive therapy, according to the Perfetti method, proposes exercises that challenge motor, sensory as well as cognitive functions of neurologically impaired patients. At the level of the hand, neurocognitive exercises typically involve haptic exploration and interaction with objects of various shapes and mechanical properties. Haptic devices are thus an ideal support to provide neurocognitive exercises under well-controlled and reproducible conditions, and to objectively assess patient performance. Here we present three neurocognitive robot-assisted exercises which were implemented on the ReHapticKnob, a high-fidelity two-degrees-of-freedom hand rehabilitation robot. The exercises were evaluated for feasibility and acceptance in a pilot study on five patients suffering from different neurological disorders. Results showed that all patients were able to take part in the neurocognitive robot-assisted therapy, and that the proposed therapy was well accepted by patients, as assessed through subjective questionnaires. Force/torque and position measurements provided insights on the motor strategy employed by the patients during the exploration of virtual object properties, and served as objective assessment of task performance. The fusion of the neurocognitive therapy concept with robot-assisted rehabilitation enriches therapeutic approaches through the focus on haptics, and could provide novel insights on sensorimotor impairment and recovery.