Deep learning-based code generation (DL-CG) applications have shown great potential for assisting developers in programming with human-competitive accuracy. However, the lack of transparency in such applications due to the uninterpretable nature of deep learning models makes the automatically generated programs untrustworthy. In this paper, we develop DeciX, an explanation method dedicated to deep learning-based code models. DeciX is motivated by observing two unique properties of DL-CG applications: output-to-output dependencies and irrelevant value and semantic space. These properties violate the fundamental assumptions made in existing explainable DL techniques and thus cause applying existing techniques to DL-CG applications rather pessimistic and even incorrect. DeciX addresses these two limitations by constructing a causal inference dependency graph, containing a novel method leveraging causal inference that can accurately quantify the contribution of each dependency edge in the graph to the end prediction result. Proved by extensive experiments assessing popular, widely-used DL-CG applications and several baseline methods, DeciX is able to achieve significantly better performance compared to state-of-the-art in terms of several critical performance metrics, including correctness, succinctness, stability, and overhead. Furthermore, DeciX can be applied to practical scenarios since it does not require any knowledge of the DL-CG model under explanation. We have also conducted case studies that demonstrate the applicability of DeciX in practice.