This work stems from an observed limitation of text encoders: embeddings may not be able to recognize fine-grained entities or events within encoded semantics, resulting in failed retrieval even in simple cases. To examine such behaviors, we first introduce a new evaluation dataset, CapRetrieval, in which passages are image captions and queries are phrases targeting entity or event concepts in diverse forms. Zero-shot evaluation suggests that encoders often struggle with these fine-grained matching, regardless of training sources or model size. Aiming for enhancement, we proceed to finetune encoders with our proposed data generation strategies, enabling a small 0.1B encoder to outperform the state-of-the-art 7B model. Within this process, we further uncover the granularity dilemma, a challenge for embeddings to capture fine-grained salience while aligning with overall semantics. Our dataset, code and models in this work are publicly released at https://github.com/lxucs/CapRetrieval.