Deep learning (DL) powered biomedical ultrasound imaging is an emerging research field where researchers adapt the image analysis capabilities of DL algorithms to biomedical ultrasound imaging settings. A major roadblock to wider adoption of DL powered biomedical ultrasound imaging is that acquiring large and diverse datasets is expensive in clinical settings, which is a requirement for successful DL implementation. Hence, there is a constant need for developing data-efficient DL techniques to turn DL powered biomedical ultrasound imaging into reality. In this work, we develop a data-efficient deep learning training strategy, which we named Zone Training. In Zone Training, we propose to divide the complete field of view of an ultrasound image into multiple zones associated with different regions of a diffraction pattern and then, train separate DL networks for each zone. The main advantage of Zone Training is that it requires less training data to achieve high accuracy. In this work, three different tissue-mimicking phantoms were classified by a DL network. The results demonstrated that Zone Training required a factor of 2-5 less training data to achieve similar classification accuracies compared to a conventional training strategy.