The diverging evidence for functional localization of response inhibition within the prefrontal cortex might be justified by the still unclear involvement of other intrinsically related cognitive processes like response selection and sustained attention. In this study, the main aim was to understand whether inhibitory impairments, previously found in patients with both left and right frontal lesions, could be better accounted for by assessing these potentially related cognitive processes. We tested 37 brain tumor patients with left prefrontal, right prefrontal and non-prefrontal lesions and a healthy control group on Go/No-Go and Foreperiod tasks. In both types of tasks inhibitory impairments are likely to cause false alarms, although additionally the former task requires response selection and the latter target detection abilities. Irrespective of the task context, patients with right prefrontal damage showed frequent Go and target omissions, probably due to sustained attention lapses. Left prefrontal patients, on the other hand, showed both Go and target omissions and high false alarm rates to No-Go and warning stimuli, suggesting a decisional rather than an inhibitory impairment. An exploratory whole-brain voxel-based lesion-symptom mapping analysis confirmed the association of left ventrolateral and dorsolateral prefrontal lesions with target discrimination failure, and right ventrolateral and medial prefrontal lesions with target detection failure. Results from this study show how left and right prefrontal areas, which previous research has linked to response inhibition, underlie broader cognitive control processes, particularly involved in response selection and target detection. Based on these findings, we suggest that successful inhibitory control relies on more than one functionally distinct process which, if assessed appropriately, might help us to better understand inhibitory impairments across different pathologies.