Large language models (LLMs) show great capabilities in generating code from natural language descriptions, bringing programming power closer to non-technical users. However, their lack of expertise in operating the generated code remains a key barrier to realizing customized applications. Function-as-a-Service (FaaS) platforms offer a high level of abstraction for code execution and deployment, allowing users to run LLM-generated code without requiring technical expertise or incurring operational overhead. In this paper, we present LLM4FaaS, a no-code application development approach that integrates LLMs and FaaS platforms to enable non-technical users to build and run customized applications using only natural language. By deploying LLM-generated code through FaaS, LLM4FaaS abstracts away infrastructure management and boilerplate code generation. We implement a proof-of-concept prototype based on an open-source FaaS platform, and evaluate it using real prompts from non-technical users. Experiments with GPT-4o show that LLM4FaaS can automatically build and deploy code in 71.47% of cases, outperforming a non-FaaS baseline at 43.48% and an existing LLM-based platform at 14.55%, narrowing the gap to human performance at 88.99%. Further analysis of code quality, programming language diversity, latency, and consistency demonstrates a balanced performance in terms of efficiency, maintainability and availability.