We present one year of optical and near-infrared photometry and spectroscopy of the Type IIP SNe 2013K and 2013am . Both objects are affected by significant extinction , due to their location in dusty regions of their respective host galaxies , ESO 009-10 and NGC 3623 ( M65 ) . From the photospheric to nebular phases , these objects display spectra congruent with those of underluminous Type IIP SNe ( i.e . the archetypal SNe 1997D or 2005cs ) , showing low photospheric velocities ( \sim 2 \times 10 ^ { 3 } km s ^ { -1 } at 50 d ) together with features arising from Ba II which are particularly prominent in faint SNe IIP . The peak V -band magnitudes of SN 2013K ( -15.6 mag ) and SN 2013am ( -16.2 mag ) are fainter than standard-luminosity Type IIP SNe . The ejected Nickel masses are 0.012 \pm 0.010 and 0.015 \pm 0.006 M _ { \odot } for SN 2013K and SN 2013am , respectively . The physical properties of the progenitors at the time of explosion are derived through hydrodynamical modelling . Fitting the bolometric curves , the expansion velocity and the temperature evolution , we infer total ejected masses of 12 and 11.5 M _ { \odot } , pre-SN radii of \sim 460 and \sim 360 R _ { \odot } , and explosion energies of 0.34 foe and 0.40 foe for SN 2013K and SN 2013am . Late time spectra are used to estimate the progenitor masses from the strength of nebular emission lines , which turn out to be consistent with red supergiant progenitors of \sim 15 M _ { \odot } . For both SNe , a low-energy explosion of a moderate-mass red supergiant star is therefore the favoured scenario .