Accurate diagnosis of disease often depends on the exhaustive examination of Whole Slide Images (WSI) at microscopic resolution. Efficient handling of these data-intensive images requires lossy compression techniques. This paper investigates the limitations of the widely-used JPEG algorithm, the current clinical standard, and reveals severe image artifacts impacting diagnostic fidelity. To overcome these challenges, we introduce a novel deep-learning (DL)-based compression method tailored for pathology images. By enforcing feature similarity of deep features between the original and compressed images, our approach achieves superior Peak Signal-to-Noise Ratio (PSNR), Multi-Scale Structural Similarity Index (MS-SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) scores compared to JPEG-XL, Webp, and other DL compression methods.