In the era of data proliferation, efficiently sifting through vast information to extract meaningful insights has become increasingly crucial. This paper addresses the computational and resource inefficiencies prevalent in existing Sequential Recommender Systems (SRSs). However, existing SRSs are often plagued by significant computational overhead and resource inefficiency during the inference stage. To address these challenges, we introduce an innovative approach combining pruning methods with advanced model designs. Furthermore, we delve into resource-constrained Neural Architecture Search (NAS), an emerging technique in recommender systems, to optimize models in terms of FLOPs, latency, and energy consumption while maintaining or enhancing accuracy. Our principal contribution is the development of a Data-aware Neural Architecture Search for Recommender System (DNS-Rec). DNS-Rec is specifically designed to tailor compact network architectures for attention-based SRS models, thereby ensuring accuracy retention. It incorporates data-aware gates to enhance the performance of the recommendation network by learning information from historical user-item interactions. Moreover, DNS-Rec employs a dynamic resource constraint strategy, stabilizing the search process and yielding more suitable architectural solutions. We demonstrate the effectiveness of our approach through rigorous experiments conducted on three benchmark datasets, which highlight the superiority of DNS-Rec in SRSs. Our findings set a new standard for future research in efficient and accurate recommendation systems, marking a significant step forward in this rapidly evolving field.