In executable task-oriented semantic parsing, the system aims to translate users' utterances in natural language to machine-interpretable programs (API calls) that can be executed according to pre-defined API specifications. With the popularity of Large Language Models (LLMs), in-context learning offers a strong baseline for such scenarios, especially in data-limited regimes (Hu et al., 2022;. However, LLMs are known to hallucinate and therefore pose a formidable challenge in constraining generated content (Parikh et al., 2020). Thus, it remains uncertain if LLMs can effectively perform task-oriented utterance-to-API generation where respecting API's structural and task-specific constraints is crucial. In this work, we seek to measure, analyze and mitigate such constraints violations. First, we identify the categories of various constraints in obtaining API-semantics from task-oriented utterances, and define fine-grained metrics that complement traditional ones. Second, we leverage these metrics to conduct a detailed error analysis of constraints violations seen in state-of-theart LLMs, which motivates us to investigate two popular mitigation strategies-Semantic-Retrieval of Demonstrations (SRD) and APIaware Constrained Decoding (API-CD). Our experiments show that these strategies are effective at reducing constraints violations and improving the quality of the generated API calls, but require careful consideration given their implementation complexity and latency.