In this paper, we propose a fully automatic method for segmentation of left ventricle, right ventricle and myocardium from cardiac Magnetic Resonance (MR) images using densely connected fully convolutional neural network. Dense Convolutional neural network (DenseNet) facilitates multi-path flow for gradients between layers during training by back-propagation and feature propagation. DenseNet also encourages feature reuse & thus substantially reduces the number of parameters while maintaining good performance, which is ideal in scenarios with limited data. The training data was subjected to Fourier analysis and classical computer vision (CV) techniques for Region of Interest (ROI) extraction. The parameters of the network were optimized by training with a dual cost function i.e. weighted cross-entropy and Dice co-efficient. For the task of automated heart diagnosis, cardiac parameters such as ejection fraction, volumes of ventricles etc. where calculated from segmentation masks predicted by the network at the end systole and diastole phases. Further these parameters were used as features to train a Random forest classifier. On the exclusively held-out test set (10% of training set) the proposed method for segmentation task achieved a mean dice score of 0.92, 0.87 and 0.86 for left ventricle, right ventricle and myocardium respectively. For automated cardiac disease diagnosis, the Random Forest classifier achieved an accuracy of 90%.