Alcohol hangover is associated with the development of alcohol use disorders, yet few studies have examined the influence of hangover on cognitive processes that may contribute towards future alcohol consumption such as response inhibition and attentional bias towards alcohol-related stimuli. Therefore, the current study aimed to explore the effects of hangover on these processes. In total, 37 adult drinkers who reported regularly engaging in heavy episodic drinking and experiencing a hangover at least once in the previous month took part in this within-subjects, “naturalistic” crossover study. Participants completed Go/No-Go (assessing response inhibition) and Visual Dot Probe (attentional bias) tasks in a hangover condition (morning following alcohol consumption) and a no-hangover condition (no alcohol consumption for at least 24 h). Participants also completed measures of hangover severity, mood, and perceived mental effort. Results indicated impaired response inhibition during hangover compared to the no-hangover condition (p < 0.001, d = 0.89), but no difference in attentional bias scores between conditions. Participants reported expending greater mental effort to complete tasks (p < 0.001, d = 1.65), decreased alertness (p < 0.001, d = 3.19), and reduced feelings of tranquillity (p < 0.001, d = 1.49) in the hangover versus no-hangover condition. Together, these findings suggest that alcohol hangover is associated with impaired response inhibition and lower mood. However, problems with recording eye-tracking data on the Visual Dot Probe task used in the present study may limit the reliability of our attentional bias findings.