We exploit the high efficiency of Langmuir-Taylor surface ionization detectors to measure by beam depletion the electronic absorption spectra of alkali atoms attached to H-2 and He clusters. Li, Na, and K atoms attached to large (H-2)(N) and (D-2)(N) clusters (N approximate to 10(3)-10(4)) have been studied at Various ortho/para concentrations in an attempt to correlate the properties of the matrix to the observed spectral features. The results are compared to theoretical predictions and to measurements done by means of conventional matrix isolation spectroscopy in bulk hydrogen. While some similarities are found, several discrepancies remain and are discussed. In the case of helium clusters, beam depletion spectra are very similar to, and in one case identical with, the laser-induced fluorescence spectra measured previously in our laboratory, revealing the total absence of quenching processes. In contrast to this, for alkali atoms attached to hydrogen clusters, quenching processes appear to dominate, and beam depletion spectra are totally different from their laser-induced fluorescence counterparts.