Sequential Recommender Systems (SRS) are extensively applied across various domains to predict users' next interaction by modeling their interaction sequences. However, these systems typically grapple with the long-tail problem, where they struggle to recommend items that are less popular. This challenge results in a decline in user discovery and reduced earnings for vendors, negatively impacting the system as a whole. Large Language Model (LLM) has the potential to understand the semantic connections between items, regardless of their popularity, positioning them as a viable solution to this dilemma. In our paper, we present LLMEmb, an innovative technique that harnesses LLM to create item embeddings that bolster the performance of SRS. To align the capabilities of general-purpose LLM with the needs of the recommendation domain, we introduce a method called Supervised Contrastive Fine-Tuning (SCFT). This method involves attribute-level data augmentation and a custom contrastive loss designed to tailor LLM for enhanced recommendation performance. Moreover, we highlight the necessity of incorporating collaborative filtering signals into LLM-generated embeddings and propose Recommendation Adaptation Training (RAT) for this purpose. RAT refines the embeddings to be optimally suited for SRS. The embeddings derived from LLMEmb can be easily integrated with any SRS model, showcasing its practical utility. Extensive experimentation on three real-world datasets has shown that LLMEmb significantly improves upon current methods when applied across different SRS models.