While the importance of supernova feedback in galaxies is well established, its role on the scale of molecular clouds is still debated. In this work, we focus on the impact of supernovae on individual clouds, using a high-resolution magneto-hydrodynamic simulation of a region of 250 pc where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae that are the natural evolution of the resolved massive stars, so their position and timing are self-consistent. We select a large sample of molecular clouds from the simulation to investigate the supernova energy injection and the resulting properties of molecular clouds. We find that molecular clouds have a lifetime of a few dynamical times, less then half of them contract to the point of becoming gravitationally bound, and the dispersal time of bound clouds, of order one dynamical time, is a factor of two shorter than that of unbound clouds. We stress the importance of internal supernovae, that is massive stars that explode inside their parent cloud, in setting the cloud dispersal time, and their huge overdensity compared to models where the supernovae are randomly distributed. We also quantify the energy injection efficiency of supernovae as a function of supernova distance to the clouds. We conclude that intermittent driving by supernovae can maintain molecular-cloud turbulence and may be the main process of cloud dispersal. The role of supernovae in the evolution of molecular clouds cannot be fully accounted for without a self-consistent implementation of their feedback.