Evaluating the quality of machine-generated natural language content is a challenging task in Natural Language Processing (NLP). Recently, large language models (LLMs) like GPT-4 have been employed for this purpose, but they are computationally expensive due to the extensive token usage required by complex evaluation prompts. In this paper, we propose a prompt optimization approach that uses a smaller, fine-tuned language model to compress input data for evaluation prompt, thus reducing token usage and computational cost when using larger LLMs for downstream evaluation. Our method involves a two-stage fine-tuning process: supervised fine-tuning followed by preference optimization to refine the model's outputs based on human preferences. We focus on Machine Translation (MT) evaluation and utilize the GEMBA-MQM metric as a starting point. Our results show a $2.37\times$ reduction in token usage without any loss in evaluation quality. This work makes state-of-the-art LLM-based metrics like GEMBA-MQM more cost-effective and efficient, enhancing their accessibility for broader use.