A major issue in translation of the artificial intelligence platforms for automatic segmentation of echocardiograms to clinics is their generalizability. The present study introduces and verifies a novel generalizable and efficient fully automatic multi-label segmentation method for four-chamber view echocardiograms based on deep fully convolutional networks (FCNs) and adversarial training. For the first time, we used generative adversarial networks for pixel classification training, a novel method in machine learning not currently used for cardiac imaging, to overcome the generalization problem. The method's performance was validated against manual segmentations as the ground-truth. Furthermore, to verify our method's generalizability in comparison with other existing techniques, we compared our method's performance with a state-of-the-art method on our dataset in addition to an independent dataset of 450 patients from the CAMUS (cardiac acquisitions for multi-structure ultrasound segmentation) challenge. On our test dataset, automatic segmentation of all four chambers achieved a dice metric of 92.1%, 86.3%, 89.6% and 91.4% for LV, RV, LA and RA, respectively. LV volumes' correlation between automatic and manual segmentation were 0.94 and 0.93 for end-diastolic volume and end-systolic volume, respectively. Excellent agreement with chambers' reference contours and significant improvement over previous FCN-based methods suggest that generative adversarial networks for pixel classification training can effectively design generalizable fully automatic FCN-based networks for four-chamber segmentation of echocardiograms even with limited number of training data.