Contrastive Language-Image Pretraining (CLIP) achieves strong generalization in vision-language tasks by aligning images and texts in a shared embedding space. However, recent findings show that CLIP-like models still underutilize fine-grained semantic signals in text, and this issue becomes even more pronounced when dealing with long and detailed captions. This stems from CLIP's training objective, which optimizes only global image-text similarity and overlooks token-level supervision - limiting its ability to achieve fine-grained visual-text alignment. To address this, we propose SuperCLIP, a simple yet effective framework that augments contrastive learning with classification-based supervision. By adding only a lightweight linear layer to the vision encoder, SuperCLIP leverages token-level cues to enhance visual-textual alignment - with just a 0.077% increase in total FLOPs, and no need for additional annotated data. Experiments show that SuperCLIP consistently improves zero-shot classification, image-text retrieval, and purely visual tasks. These gains hold regardless of whether the model is trained on original web data or rich re-captioned data, demonstrating SuperCLIP's ability to recover textual supervision in both cases. Furthermore, SuperCLIP alleviates CLIP's small-batch performance drop through classification-based supervision that avoids reliance on large batch sizes. Code and models will be made open source.