Research on cell-cell communication (CCC) is crucial for understanding biology and diseases. Many existing CCC inference tools neglect potential confounders, such as batch and demographic variables, when analyzing multi-sample, multi-condition scRNA-seq datasets. To address this significant gap, we introduce STACCato, a Supervised Tensor Analysis tool for studying Cell-cell Communication, that identifies CCC events and estimates the effects of biological conditions (e.g., disease status, tissue types) on such events, while adjusting for potential confounders. Application of STACCato to both simulated data and real scRNA-seq data of lupus and autism studies demonstrate that incorporating sample-level variables into CCC inference consistently provides more accurate estimations of disease effects and cell type activity patterns than existing methods that ignore sample-level variables. A computational tool implementing the STACCato framework is available on GitHub.