We present Robot-centric Pooling (RcP), a novel pooling method designed to enhance end-to-end visuomo-tor policies by enabling differentiation between the robots and similar entities or their surroundings. Given an image-proprioception pair, RcP guides the aggregation of image features by highlighting image regions correlating with the robot's proprioceptive states, thereby extracting robot-centric image representations for policy learning. Leveraging contrastive learning techniques, RcP integrates seamlessly with existing visuomotor policy learning frameworks and is trained jointly with the policy using the same dataset, requiring no extra data collection involving self-distractors. We evaluate the proposed method with reaching tasks in both simulated and real-world settings. The results demonstrate that RcP significantly enhances the policies' robustness against various unseen distractors, including self-distractors, positioned at different locations. Additionally, the inherent robot-centric characteristic of RcP enables the learnt policy to be far more resilient to aggressive pixel shifts compared to the baselines. Code available at: https://github.com/Zheyu-Zhuang/RcP