How low clouds respond to warming constitutes a key uncertainty for climate projections. Here we observationally constrain low‐cloud feedback through a controlling factor analysis based on ridge regression. We find a moderately positive global low‐cloud feedback (0.45 W , 90% range 0.18–0.72 W ), about twice the mean value (0.22 W ) of 16 models from the Coupled Model Intercomparison Project. We link this discrepancy to a pervasive model mean‐state bias: models underestimate the low‐cloud response to warming because (a) they systematically underestimate present‐day tropical marine low‐cloud amount, and (b) the low‐cloud sensitivity to warming is proportional to this present‐day low‐cloud amount. Our results hence highlight the importance of reducing model biases in both the mean state of clouds and their sensitivity to environmental factors for accurate climate change projections.