Currently, the lack of awareness of deficits, i.e., anosognosia, is a major obstacle in the healthcare circuit that delays the diagnosis of Alzheimer's disease (AD). However, a clear framework is lacking in the literature related to this phenomenon in terms of its definition, mechanisms, and objects. The aim of this study is to assess the different levels of cognitive anosognosia using a prediction-performance procedure and to identify the potential correlates of these levels. A sample of patients with probable AD was divided into three groups according to the severity of dementia (mild (MiD), moderate (MoD), and moderately severe (MSD) dementia), ranked according to the results of the Mini-Mental State Examination. We observed the following three scores: the real score, the prediction score, and the anosognosia score. These scores were calculated based on the prediction-performance task MISAwareness from the Dementia Rating Scale for cognitive processes (i.e., Attention, Initiation, Conceptualization, Construction, and Memory). We obtained a strong plateau effect between the MiD and MoD groups for anosognosia scores for actual performance or prediction for both the level of overall functioning and for specific processes. The sole exception was the result for memory processes. Moreover, the profiles of the patients' responses on the Memory subscale were substantially different and, indeed, opposite from those for the other processes. The main results confirm the multidimensionality of anosognosia and its variability with the stage of dementia and specifically implicate memory processes that indicate a cleavage between memory and other cognitive functions.