© 2016 CERN. The differential cross sections for inclusive neutral pions as a function of transverse and longitudinal momentum in the very forward-rapidity region have been measured at the LHC with the LHC forward detector in proton-proton collisions at s=2.76 and 7 TeV and in proton-lead collisions at nucleon-nucleon center-of-mass energies of sNN=5.02 TeV. Such differential cross sections in proton-proton collisions are compatible with the hypotheses of limiting fragmentation and Feynman scaling. Comparing proton-proton with proton-lead collisions, we find a sizable suppression of the production of neutral pions in the differential cross sections after subtraction of ultraperipheral proton-lead collisions. This suppression corresponds to the nuclear modification factor value of about 0.1-0.3. The experimental measurements presented in this paper provide a benchmark for the hadronic interaction Monte Carlo simulation codes that are used for the simulation of cosmic ray air showers.