Positive and negative feedback loops, for example, where a protein regulates its own transcription, play an important role in many genetic regulatory networks. Such systems will be subject to internal noise, which occurs due to the small number of molecules taking part in some reactions. This paper examines the effect of feedback loops on noise levels. Error growth techniques from nonlinear dynamics are used to estimate the variance of a system around a steady-state attractor. It is shown that variablity due to intrinsic stochasticity is directly linked to the stability of the steady state, and therefore to the system's resistance to external perturbations. The methods are demonstrated for a number of simple systems, including a genetic switch with homo-dimerizing regulatory protein, and an oscillator.