Deep Reinforcement Learning (DRL) has achieved impressive performance in robotics and autonomous systems (RAS). A key challenge to its deployment in real-life operations is the presence of spuriously unsafe DRL policies. Unexplored states may lead the agent to make wrong decisions that could result in hazards, especially in applications where DRL-trained end-to-end controllers govern the behaviour of RAS. This paper proposes a novel quantitative reliability assessment framework for DRL-controlled RAS, leveraging verification evidence generated from formal reliability analysis of neural networks. A two-level verification framework is introduced to check the safety property with respect to inaccurate observations that are due to, e.g., environmental noise and state changes. Reachability verification tools are leveraged locally to generate safety evidence of trajectories. In contrast, at the global level, we quantify the overall reliability as an aggregated metric of local safety evidence, corresponding to a set of distinct tasks and their occurrence probabilities. The effectiveness of the proposed verification framework is demonstrated and validated via experiments on real RAS.