Computer-assisted diagnosis (CAD) plays a key role in cancer diagnosis or screening. Whereas, current CAD performs poorly on whole slide image (WSI) analysis, and thus fails to generalize well. This research aims to develop an automatic classification system to distinguish between different types of carcinomas. Obtaining rich deep features in multi-class classification while achieving high accuracy is still a challenging problem. The detection and classification of cancerous cells in WSI are quite challenging due to the misclassification of normal lumps and cancerous cells. This is due to cluttering, occlusion, and irregular cell distribution. Researchers in the past mostly obtained the hand-crafted features while neglecting the above-mentioned challenges which led to a reduction of the classification accuracy. To mitigate this problem we proposed an efficient dual attention-based network (CytoNet). The proposed network is composed of two main modules (i) Efficient-Net and (ii) Dual Attention Module (DAM). Efficient-Net is capable of obtaining higher accuracy and enhancing efficiency as compared to existing Convolutional Neural Networks (CNNs). It is also useful to obtain the most generic features as it has been trained on ImageNet. Whereas DAM is very robust in obtaining attention and targeted features while negating the background. In this way, the combination of an efficient and attention module is useful to obtain the robust, and intrinsic features to obtain comparable performance. Further, we evaluated the proposed network on two well-known datasets (i) Our generated thyroid dataset (ii) Mendeley Cervical dataset (Hussain in Data Brief, 2019) with enhanced performance compared to their counterparts. CytoNet demonstrated a 99% accuracy rate on the thyroid dataset in comparison to its counterpart. The precision, recall, and F1-score values achieved on the Mendeley Cervical dataset are 0.992, 0.985, and 0.977, respectively. The code implementation is available on GitHub. https://github.com/naveedilyas/CytoNet-An-Efficient-Dual-Attention-based-Automatic-Prediction-of-Cancer-Sub-types-in-Cytol.