We investigate the lasing modes in diffusive random media with local pumping. The reabsorption of emitter light suppresses the feedback from the unpumped part of the sample and effectively reduces the system size. The lasing modes are dramatically different from the quasimodes of the passive system (without gain or absorption). Even if all the quasimodes of a passive diffusive system are extended across the entire sample, the lasing modes are still confined in the pumped volume with an exponential tail outside it. The reduction of effective system volume by absoption broadens the distribution of decay rates of quasimodes and facilitates the occurrence of discrete lasing peaks.