Brain-computer interfaces (BCI), 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. Most of these studies show the presence of ErrP in typical choice reaction tasks where subjects respond to a stimulus and ErrP arise following errors due to the subject's incorrect motor action. However, in the context of a BCI, the central question is: "Are ErrP also elicited when the error is made by the interface during the recognition of the subject's intent?" We have thus explored whether ErrP also follow a feedback indicating incorrect responses of the interface and no longer errors of the subject himself. Four healthy volunteer subjects participated in a simple human-robot interaction experiment (i.e., bringing the robot to either the left or right side of a room), which seem to reveal a new kind of ErrP. These "interaction ErrP" exhibit a first sharp negative peak followed by a broader positive peak and a second negative peak (~270, 400 and 550 ms after the feedback, respectively). But in order to exploit these ErrP we need to detect it in each single trial using a short window following the feedback that shows the response of the classifier embedded in the BCI. We have achieved an average recognition rate of correct and erroneous single trials of 83.7% and 80.2%, respectively. We also show that the integration of these ErrP in a BCI, where the subject's intent is not executed if an ErrP is detected, significantly improves the performance of the BCI.