We consider, both theoretically and experimentally, the excitation and detection of the localized quasimodes (resonances) in an open dissipative 1D random system. We show that, even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonance characteristics inside the random system exclusively from reflection measurements.