Isogenic cells in culture show strong variability, which arises from dynamic adaptations to the microenvironment of individual cells. Here we study the influence of the cell population context, which determines a single cell's microenvironment, in image-based RNAi screens. We developed a comprehensive computational approach that employs Bayesian and multivariate methods at the single-cell level. We applied these methods to 45 RNA interference screens of various sizes, including 7 druggable genome and 2 genome-wide screens, analysing 17 different mammalian virus infections and four related cell physiological processes. Analysing cell-based screens at this depth reveals widespread RNAi-induced changes in the population context of individual cells leading to indirect RNAi effects, as well as perturbations of cell-to-cell variability regulators. We find that accounting for indirect effects improves the consistency between siRNAs targeted against the same gene, and between replicate RNAi screens performed in different cell lines, in different labs, and with different siRNA libraries. In an era where large-scale RNAi screens are increasingly performed to reach a systems-level understanding of cellular processes, we show that this is often improved by analyses that account for and incorporate the single-cell microenvironment.