A reliable representation of the mechanisms leading to decadal variability in climate models is crucial for projections of multi-year droughts and other long-lasting extremes. Here we show that CMIP6 climate models have  too low autocorrelation at one-year time lag and beyond, and as a result too weak decadal variability in both precipitation and sea level pressure (SLP). We employ a statistical learning technique to systematically quantify the extent to which SSTs condition the anomalies in these surface variables across the globe. In the extratropics, SSTs explain only a small portion of the variability of precipitation and SLP in models, even at multi-year time scales. ERA5 and 20CRv3 reanalyses suggest distinctly higher autocorrelation and decadal variability because of a stronger conditioning by SSTs in the real world. We attribute the weak decadal variability of precipitation and SLP in models to a weak dynamical atmospheric response to decadal variability of SSTs. Our results suggest that the models considered underestimate the dynamical ocean-atmosphere coupling that is important for decadal variability in extratropical precipitation and SLP, especially outside the regions impacted by the sub-decadal tropical Pacific ocean variability.