We present a numerical study of lasing modes in diffusive random media with local pumping. The reabsorption of emitted 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 quasi modes of the passive system (without gain or absorption). Even if all the quasi modes 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 absorption broadens the distribution of decay rates of quasi modes and facilitates the occurrence of discrete lasing peaks.