Recent advances in Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) have enabled diverse retrieval methods. However, existing retrieval methods often fail to accurately retrieve results for negation and exclusion queries. To address this limitation, prior approaches rely on embedding adaptation or fine-tuning, which introduce additional computational cost and deployment complexity. We propose Direct Embedding Optimization (DEO), a training-free method for negation-aware text and multimodal retrieval. DEO decomposes queries into positive and negative components and optimizes the query embedding with a contrastive objective. Without additional training data or model updates, DEO outperforms baselines on NegConstraint, with gains of +0.0738 nDCG@10 and +0.1028 MAP@100, while improving Recall@5 by +6\% over OpenAI CLIP in multimodal retrieval. These results demonstrate the practicality of DEO for negation- and exclusion-aware retrieval in real-world settings.