The use of large language models (LLMs) as evaluators has garnered significant attention due to their potential to rival human-level evaluations in long-form response assessments. However, current LLM evaluators rely heavily on static, human-defined criteria, limiting their ability to generalize across diverse generative tasks and incorporate context-specific knowledge. In this paper, we propose a novel Self-Assessing LLM framework that integrates Context-Aware Criteria (SALC) with dynamic knowledge tailored to each evaluation instance. This instance-level knowledge enhances the LLM evaluator's performance by providing relevant and context-aware insights that pinpoint the important criteria specific to the current instance. Additionally, the proposed framework adapts seamlessly to various tasks without relying on predefined human criteria, offering a more flexible evaluation approach. Empirical evaluations demonstrate that our approach significantly outperforms existing baseline evaluation frameworks, yielding improvements on average 4.8% across a wide variety of datasets. Furthermore, by leveraging knowledge distillation techniques, we fine-tuned smaller language models for criteria generation and evaluation, achieving comparable or superior performance to larger models with much lower cost. Our method also exhibits a improvement in LC Win-Rate in AlpacaEval2 leaderboard up to a 12% when employed for preference data generation in Direct Preference Optimization (DPO), underscoring its efficacy as a robust and scalable evaluation framework.