Pacific decadal variability (PDV), low-frequency changes in Pacific sea surface temperatures (SSTs), significantly impacts global climate. However, disentangling anthropogenic effects upon PDV is challenging since both vary on similar time scales. Using single-forcing climate model large ensembles, we find that anthropogenic forcing primarily drives a spatially-varying pattern of mean-state change in North Pacific SST that project onto leading PDV patterns, principally the Pacific Decadal Oscillation (PDO) and North Pacific Gyre Oscillation (NPGO). In fact, when the trend is determined by the model ensemble mean, there is no forced change of the PDV modes. However, analysis of single model realizations, where the mean-state trend cannot be cleanly identified, suggests an apparent anthropogenic change in NPGO decadal variability. This suggests that observed PDV responses to anthropogenic forcing may be erroneously convolved with the background trend pattern. Therefore, correctly determining the mean-state trend is a necessary precursor for identifying forced changes to PDV.