Compulsivity is a core symptom in different psychopathological disorders, characterized by excessive behaviors and behavioral inflexibility. The selection of high drinker (HD) versus low drinker (LD) rats by schedule-induced polydipsia (SIP) is a valid model for studying the compulsive phenotype. The compulsive HD rats showed cognitive inflexibility and reduced serotonin 2A (5-HT2A) receptor binding levels in the frontal cortex (FC). According to that, we hypothesize that compulsive HD rats might have an alteration in the cognitive control domain regarding inflexibility, assessed by spatial memory on the Morris Water Maze (MWM), working and reference memory by the Radial Arm Maze, and behavioral deficits in stimulus processing by the Novel Object Recognition test. The possible underlying mechanisms might be linked to the brain gene expression of 5HT2A, 5HT2C, glutamate NMDA receptors, and brain-derived neurotrophic factor (BDNF) in FC, hippocampus, and amygdala. HD rats confirmed a cognitive inflexibility profile on the reversal condition in the MWM compared to LD rats, while no differences were observed on stimulus processing, spatial, and working memory. Moreover, HD rats showed a reduced expression of the Htr2a, Grin1, and Bdnf genes in FC. Furthermore, there was a negative correlation between the relative expression of the Htr2a, Grin1, and Bdnf genes in FC and the level of compulsive water intake in HD rats on SIP. These data reveal that cognitive inflexibility may not be associated with a memory or stimulus processing deficit in compulsive individuals but may result by a region-specific alteration of the Htr2a, Grin1, and Bdnf gene expression in FC.