The evaluation of cardiac contractility by the assessment of the ventricular systolic elastance function is clinically challenging and cannot be easily obtained at the bedside. In this work, we present a framework characterizing left ventricular systolic function from clinically readily available data, including systemic and pulmonary arterial pressure signals. We implemented and calibrated a deep neural network (DNN) consisting of a multi-layer perceptron with 4 fully connected hidden layers and with 16 neurons per layer, which was trained with data obtained from a lumped model of the cardiovascular system modeling different levels of cardiac function. The lumped model included a function of circulatory autoregulation from carotid baroreceptors in pulsatile conditions. Inputs for the DNN were systemic and pulmonary arterial pressure curves. Outputs from the DNN were parameters of the lumped model characterizing left ventricular systolic function, especially end-systolic elastance. The DNN adequately performed and accurately recovered the relevant hemodynamic parameters with a mean relative error of less than 2%. Therefore, our framework can easily provide complex physiological parameters of cardiac contractility, which could lead to the development of invaluable tools for the clinical evaluation of patients with severe cardiac dysfunction.