We introduce (and test on real data) a new method based on Machine Learning techniques to quantitatively analyse observed microlensing light curves of lensed quasars. The method is aimed at providing a fast and robust procedure to estimate physical parameters from observed light curves, in order to be easily applied to the large quantities of light curves expected in future surveys. We introduce a set of features (mostly of statistical nature, although some also consider time correlation to measure the slope and waviness) that characterize a light curve, and which are used to train suitable supervised learning models with mock data. The trained models can therefore be used to predict important physical quantities when applied to the observed microlensing light curves. We first show the robustness and speed of the method on mock data, showing the excellent accuracy/performance even when applied to physical models different to the trained one. We show that the used set of features is robust against noise and irregular sampling. The used features can be easily expanded, and the learning model can be changed to suit different needs. We provide a general recipe to systematically apply this methodology to observed light curves to estimate accretion disc sizes. Finally, we test the method on real data with the OGLE light curves of the well known system Q2237+0305, showing very good results, in agreement with previous ones in the literature. This method provides a new alternative powerful and promising technique to extract physical information from microlensing light curves of lensed quasars.