Treatment of patients with obstructive coronary artery disease is guided by the functional significance of a coronary artery stenosis. Fractional flow reserve (FFR), measured during invasive coronary angiography (ICA), is considered the gold standard to define the functional significance of a coronary stenosis. Here, we present a method for non-invasive detection of patients with functionally significant coronary artery stenosis, combining analysis of the coronary artery tree and the left ventricular (LV) myocardium in cardiac CT angiography (CCTA) images. We retrospectively collected CCTA scans of 126 patients who underwent invasive FFR measurements, to determine the functional significance of coronary stenoses. We combine our previous works for the analysis of the complete coronary artery tree and the LV myocardium: Coronary arteries are encoded by two disjoint convolutional autoencoders (CAEs) and the LV myocardium is characterized by a convolutional neural network (CNN) and a CAE. Thereafter, using the extracted encodings of all coronary arteries and the LV myocardium, patients are classified according to the presence of functionally significant stenosis, as defined by the invasively measured FFR. To handle the varying number of coronary arteries in a patient, the classification is formulated as a multiple instance learning problem and is performed using an attention-based neural network. Cross-validation experiments resulted in an average area under the receiver operating characteristic curve of $0.74 \pm 0.01$, and showed that the proposed combined analysis outperformed the analysis of the coronary arteries or the LV myocardium only. The results demonstrate the feasibility of combining the analyses of the complete coronary artery tree and the LV myocardium in CCTA images for the detection of patients with functionally significant stenosis in coronary arteries.