Modeling and simulation of biochemical systems are some of the important research areas in the rapid rise of Systems Biology. Often biochemical kinetic models represent cellular processes as systems of chemical reactions. The dynamics of these systems is typically described by using stochastic models. We introduce a method for an accurate sensitivity analysis of continuous such models of well-stirred biochemical systems. Sensitivity analysis plays a central role in the study of biochemical systems, being an important tool in their model construction, investigation and validation. In particular, it enables the identification of the key reaction rate parameters and it gives insight on how to effectively reduce the system while maintaining its overall behavior. The efficiency and accuracy of the method discussed are tested on several examples of practical interest.