Several studies have probed perceptual performance at different times after a self-paced motor action and found frequency-specific modulations of perceptual performance phase-locked to the action. Such action-related modulation has been reported for various frequencies and modulation strengths. In an attempt to establish a basic effect at the population level, we had a relatively large number of participants (n=50) perform a self-paced button press followed by a detection task at threshold, and we applied both fixed- and random-effects tests. The combined data of all trials and participants surprisingly did not show any significant action-related modulation. However, based on previous studies, we explored the possibility that such modulation depends on the participant's internal state. Indeed, when we split trials based on performance in neighboring trials, then trials in periods of low performance showed an action-related modulation at approximately 17 Hz. When we split trials based on the performance in the preceding trial, we found that trials following a ''miss'' showed an action-related modulation at approximately 17 Hz. Finally, when we split participants based on their false-alarm rate, we found that participants with no false alarms showed an action-related modulation at approximately 17 Hz. All these effects were significant in random-effects tests, supporting an inference on the population. Together, these findings indicate that action-related modulations are not always detectable. However, the results suggest that specific internal states such as lower attentional engagement and/or higher decision criterion are characterized by a modulation in the beta-frequency range.