The prevention and diagnosis of frailty syndrome (FS) in cardiac patients requires innovative systems to support medical personnel, patient adherence, and self-care behavior. To do so, modern medicine uses a supervised machine learning approach (ML) to study the psychosocial domains of frailty in cardiac patients with heart failure (HF). This study aimed to determine the absolute and relative diagnostic importance of the individual components of the Tilburg Frailty Indicator (TFI) questionnaire in patients with HF. An exploratory analysis was performed using machine learning algorithms and the permutation method to determine the absolute importance of frailty components in HF. Based on the TFI data, which contain physical and psychosocial components, machine learning models were built based on three algorithms: a decision tree, a random decision forest, and the AdaBoost Models classifier. The absolute weights were used to make pairwise comparisons between the variables and obtain relative diagnostic importance. The analysis of HF patients’ responses showed that the psychological variable TFI20 diagnosing low mood was more diagnostically important than the variables from the physical domain: lack of strength in the hands and physical fatigue. The psychological variable TFI21 linked with agitation and irritability was diagnostically more important than all three physical variables considered: walking difficulties, lack of hand strength, and physical fatigue. In the case of the two remaining variables from the psychological domain (TFI19, TFI22), and for all variables from the social domain, the results do not allow for the rejection of the null hypothesis. From a long-term perspective, the ML based frailty approach can support healthcare professionals, including psychologists and social workers, in drawing their attention to the non-physical origins of HF.