We demonstrate that strong suppression of the relative production rate (d+Au)/(p+p) of inclusive high-pT hadrons at forward rapidities observed at RHIC is due to parton multiple rescatterings in nuclear matter. The light-cone dipole approach-based calculations are in a good agreement with BRAHMS and STAR data. They also indicate a significant nuclear suppression at midrapidities with a weak onset of the coherence effects. This prediction is supported by the preliminary d+Au data from the PHENIX Collaboration. Moreover, since similar suppression pattern is also expected to show up at lower energies where effects of parton saturation are not expected, we are able to exclude from the interpretation of observed phenomena models based on the Color Glass Condensate.