Accurate prediction of future human positions is an essential task for modern video-surveillance systems. Current state-of-the-art models usually rely on a "history" of past tracked locations (e.g., 3 to 5 seconds) to predict a plausible sequence of future locations (e.g., up to the next 5 seconds). We feel that this common schema neglects critical traits of realistic applications: as the collection of input trajectories involves machine perception (i.e., detection and tracking), incorrect detection and fragmentation errors may accumulate in crowded scenes, leading to tracking drifts. On this account, the model would be fed with corrupted and noisy input data, thus fatally affecting its prediction performance. In this regard, we focus on delivering accurate predictions when only few input observations are used, thus potentially lowering the risks associated with automatic perception. To this end, we conceive a novel distillation strategy that allows a knowledge transfer from a teacher network to a student one, the latter fed with fewer observations (just two ones). We show that a properly defined teacher supervision allows a student network to perform comparably to state-of-the-art approaches that demand more observations. Besides, extensive experiments on common trajectory forecasting datasets highlight that our student network better generalizes to unseen scenarios.