We study the impact of supernovae on individual molecular clouds, using a high-resolution magnetohydrodynamic simulation of a 250 pc region where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae, meaning 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 than 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 2 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 for cloud dispersal and that the full role of supernovae in the evolution of molecular clouds cannot be fully accounted for without a self-consistent implementation of the supernova feedback.