Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic analysis methods, such as Gillespie algorithm and Langevin simulation. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both intrinsic and extrinsic noises, we develop a new method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. Unlike traditional methods, RACIPE generates and analyzes an ensemble of mathematical models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. Under the framework of this randomization-based approach, here we develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several gene regulatory circuits, we found that high noise, but not large parameter variation, merges clusters together. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE into a freely available R package.