The increasing complexity and diversity of hardware accelerators in modern computing systems demand flexible, low-overhead program analysis tools. We present PASTA, a low-overhead and modular Program AnalysiS Tool Framework for Accelerators. PASTA abstracts over low-level profiling APIs and diverse deep learning frameworks, offering users a unified interface to capture and analyze runtime events at multiple levels. Its extensible design enables researchers and practitioners to rapidly prototype custom tools with minimal overhead. We demonstrate the utility of PASTA by developing several analysis tools, including a deep learning workload characterization tool and a UVM optimization tool. Through extensive evaluation on mainstream deep learning workloads tested on NVIDIA and AMD GPUs under both single- and multi-GPU scenarios, we demonstrate PASTA's broad applicability. On NVIDIA GPUs, we further show that PASTA provides detailed performance insights with significantly lower overhead, up to 1.3*10^4 faster than conventional analysis tools, thanks to its GPU-accelerated backend. PASTA strikes a practical balance between usability, extensibility, and efficiency, making it well-suited for modern accelerator-based computing environments.