While Large Language Models (LLMs) have emerged as promising tools for evaluating Natural Language Generation (NLG) tasks, their effectiveness is limited by their inability to appropriately weigh the importance of different topics, often overemphasizing minor details while undervaluing critical information, leading to misleading assessments. Our work proposes an efficient prompt design mechanism to address this specific limitation and provide a case study. Through strategic prompt engineering that incorporates explicit importance weighting mechanisms, we enhance using LLM-as-a-Judge ability to prioritize relevant information effectively, as demonstrated by an average improvement of 6% in the Human Alignment Rate (HAR) metric.