Current methods for comparing single-cell RNA sequencing datasets collected in multiple conditions focus on discrete regions of the transcriptional state space, such as clusters of cells. Here we quantify the effects of perturbations at the single-cell level using a continuous measure of the effect of a perturbation across the transcriptomic space. We describe this space as a manifold and develop a relative likelihood estimate of observing each cell in each of the experimental conditions using graph signal processing. This likelihood estimate can be used to identify cell populations specifically affected by a perturbation. We also develop vertex frequency clustering to extract populations of affected cells at the level of granularity that matches the perturbation response. The accuracy of our algorithm at identifying clusters of cells that are enriched or depleted in each condition is, on average, 57% higher than the next-best-performing algorithm tested. Gene signatures derived from these clusters are more accurate than those of six alternative algorithms in ground truth comparisons.