Brain-computer interfaces (BCIs), as any other interaction modality based on physiological signals and body channels (e.g., muscular activity, speech and gestures), are prone to errors in the recognition of subject's intent. An elegant approach to improve the accuracy of BCIs consists in a verification procedure directly based on the presence of error-related potentials (ErrP) in the EEG recorded right after the occurrence of an error. Six healthy volunteer subjects with no prior BCI experience participated in a new human-robot interaction experiment where they were asked to mentally move a cursor towards a target that can be reached within a few steps using motor imagination. This experiment confirms the previously reported presence of a new kind of ErrP. These Interaction ErrP exhibit a first sharp negative peak followed by a positive peak and a second broader negative peak (~290, ~350 and ~470 ms after the feedback, respectively). But in order to exploit these ErrP we need to detect them in each single trial using a short window following the feedback associated to the response of the classifier embedded in the BCI. We have achieved an average recognition rate of correct and erroneous single trials of 81.8% and 76.2%, respectively. Furthermore, we have achieved an average recognition rate of the subject's intent while trying to mentally drive the cursor of 73.1%. These results show that it's possible to simultaneously extract useful information for mental control to operate a brain-actuated device as well as cognitive states such as error potentials to improve the quality of the brain-computer interaction. Finally, using a well-known inverse model (sLORETA), we show that the main focus of activity at the occurrence of the ErrP are, as expected, in the pre-supplementary motor area and in the anterior cingulate cortex.