Large language model (LLM) agents have evolved to intelligently process information, make decisions, and interact with users or tools. A key capability is the integration of long-term memory capabilities, enabling these agents to draw upon historical interactions and knowledge. However, the growing memory size and need for semantic structuring pose significant challenges. In this work, we propose an autonomous memory augmentation approach, MemInsight, to enhance semantic data representation and retrieval mechanisms. By leveraging autonomous augmentation to historical interactions, LLM agents are shown to deliver more accurate and contextualized responses. We empirically validate the efficacy of our proposed approach in three task scenarios; conversational recommendation, question answering and event summarization. On the LLM-REDIAL dataset, MemInsight boosts persuasiveness of recommendations by up to 14%. Moreover, it outperforms a RAG baseline by 34% in recall for LoCoMo retrieval. Our empirical results show the potential of MemInsight to enhance the contextual performance of LLM agents across multiple tasks.