How much does environmental autocorrelation matter to the growth of structured populations in real life contexts? Interannual variances in vital rates certainly do, but it has been suggested that between-year correlations may not. We present an analytical approximation to stochastic growth rate for multistate Markovian environments and show that it is accurate by testing it in two empirically based examples. We find that temporal autocorrelation has sizeable effect on growth rates of structured populations, larger in many cases than the effect of interannual variability. Our approximation defines a sensitivity to autocorrelated variability, showing how demographic damping and environmental pattern interact to determine a population's stochastic growth rate.