Older adults are more likely than young adults to show age‐related increases in remembering events that never occurred. However, little is known about the neural mechanisms underlying the increased occurrence of false alarms in older adults. To investigate this issue, this fMRI study examined age‐related differences in correct rejection activations during the retrieval of memory for faces. In behavioral data, older adults showed a higher rate of false alarms than young adults in subjective recollection responses. From fMRI data, an age‐related decrease in brain activations during correct rejections was identified in the inferior frontal gyrus, supramarginal gyrus, and hippocampus. In addition, interaction between activations in the inferior frontal and supramarginal regions during correct rejections was significantly lower in older adults than in young adults. These findings suggest that an age‐related decline in interaction between the ventral prefrontal region, which is involved in the source monitoring process during retrieval, and the inferior parietal region, which is associated with recollection by cooperating with the hippocampus, could induce impaired differentiation between old and novel stimuli in older adults.