State-of-the-art presentation attack detection approaches tend to overfit to the presentation attack instruments seen during training and fail to generalize to unknown presentation attack instruments. Given that face presentation attack detection is inherently a local task, we propose a face presentation attack detection framework, namely Self-Supervised Regional Fully Convolutional Network (SSR-FCN), that is trained to learn local discriminative cues from a face image in a self-supervised manner. The proposed framework (i) improves generalizability while maintaining the computational efficiency of holistic face presentation attack detection approaches (<; 4 ms on a Nvidia GTX 1080Ti GPU), and (ii) is more interpretable since it localizes the parts of the face that are labeled as presentation attacks. Experimental results show that SSR-FCN can achieve TDR = 65% @ 2.0% FDR when evaluated on a dataset, SiW-M, comprising of 13 different presentation attack instruments under unknown attacks while achieving competitive performances under standard benchmark datasets (Oulu-NPU, CASIA-MFSD, and Replay-Attack).