The proliferation of diverse network services in 5G and beyond networks has led to the emergence of network slicing technologies. Among these, admission control plays a crucial role in achieving specific optimization goals through the selective acceptance of service requests. Although Deep Reinforcement Learning (DRL) forms the foundation in many admission control approaches for its effectiveness and flexibility, the initial instability of DRL models hinders their practical deployment in real-world networks. In this work, we propose a digital twin (DT) assisted DRL solution to address this issue. Specifically, we first formulate the admission decision-making process as a semi-Markov decision process, which is subsequently simplified into an equivalent discrete-time Markov decision process to facilitate the implementation of DRL methods. The DT is established through supervised learning and employed to assist the training phase of the DRL model. Extensive simulations show that the DT-assisted DRL model increased resource utilization by over 40\% compared to the directly trained state-of-the-art Dueling-DQN and over 20\% compared to our directly trained DRL model during initial training. This improvement is achieved while preserving the model's capacity to optimize the long-term rewards.