Single-cell RNA-sequencing (scRNA-seq) facilitates identification of new cell types and gene regulatory networks as well as dissection of the kinetics of gene expression and patterns of allele-specific expression. However, to facilitate such analyses, separating biological variability from the high level of technical noise that affects scRNA-seq protocols is vital. Here we describe and validate a generative statistical model that accurately quantifies technical noise with the help of external RNA spike-ins. Applying our approach to investigate stochastic allele-specific expression in individual cells, we demonstrate that a large fraction of stochastic allele-specific expression can be explained by technical noise, especially for lowly and moderately expressed genes: we predict that only 17.8% of stochastic allele-specific expression patterns are attributable to biological noise with the remainder due to technical noise.