This paper proposes a deep learning-based multi-label classification approach to detect coordinated and simultaneously launched data falsification attacks on a large number of distributed generators (DGs). The proposed approach can detect coordinated additive, deductive, and combination of additive and deductive (attackers use the combination of additive and deductive attacks to camouflage their attacks) types of power output manipulation and falsification attacks on DGs. In training the proposed classifier, readings from DG meters and data from supervisory control and data acquisition (SCADA) systems along with meteorological data are used as input and class labels (additive, deductive, and combination) are used as output. The output class labels are developed based on the comparison between normal and compromised outputs of DGs. Two parallel data falsification classifiers with separate class labels are developed to increase the detection accuracy. The proposed approach is demonstrated on several systems including a 240-node real distribution system (based in the USA) and the IEEE 123-node distribution test system. The results show that the proposed approach can detect low margin coordinated attacks (as low as 5% of actual DG readings) with up to 99.9% accuracy. The performance of the proposed work is compared with multi-layer perceptron (MLP), convolutional neural network (CNN), and residual neural network. All of the developed source codes (including unbalanced quasi-static power flow in OpenDSS-MATLAB environment and deep learning in Python) of the proposed solution are publicly available at GitHub.