Laser action in active random media in the weak scattering regime far from Anderson localization is investigated by coupling Maxwell's equations with the rate equations of a four-level atomic system. We report systematic lasing action with resonant feedback and show that the lasing modes mostly consist of traveling waves spatially extended over the whole system. Next we address the question of the origin of the feedback mechanism in such a system where no disorder-induced long-lived resonances are available, and present strong evidence that they correspond to the quasimodes of the passive system. This in turn provides an original way to access the spatial distribution of the quasimodes of a non-Hermitian system.