Hadron production in proton-nucleus (pA) collisions was previously shown to be suppressed by medium-induced fully coherent energy loss (FCEL). We show that the quenching of $D$ and $B$ mesons in pPb collisions at the LHC due solely to FCEL is, at least, on par with other nuclear effects such as gluon shadowing or saturation. This is consistent with previous findings for both quarkonium and light hadron production in pA collisions, emphasising that FCEL effects need to be included for a reliable understanding of hadron production measurements in pA collisions.