Relevant sounds such as alarms are sometimes involuntarily ignored, a phenomenon called inattentional deafness. This phenomenon occurs under specific conditions including high workload (i.e., multitasking) and/or cognitive fatigue. In the context of aviation, such an error can have drastic consequences on flight safety. This study uses an oddball paradigm in which participants had to detect rare sounds in an ecological context of simulated flight. Cognitive fatigue and cognitive load were manipulated to trigger inattentional deafness, and brain activity was recorded via electroencephalography (EEG). Our results showed that alarm omission and alarm detection can be classified based on time-frequency analysis of brain activity. We reached a maximum accuracy of 76.4% when the algorithm was trained on all participants and a maximum of 90.5%, on one participant, when the algorithm was trained individually. This method can benefit from explainable artificial intelligence to develop efficient and understandable passive brain-computer interfaces, improve flight safety by detecting such attentional failures in real time, and give appropriate feedback to pilots, according to our ambitious goal, providing them with reliable and rich human/machine interactions.