Atmospheric neutrinos, produced by cosmic ray interactions, are a unique probe to study neutrino oscillations and exotic phenomena beyond the Standard Model, as well as the main background to measurements of astrophysical neutrinos. Due to the higher precision of next generation detectors, flux uncertainties are increasingly impacting such studies, in particular driven by the lack of measurements from hadronic particle production in the very forward region. In this work we introduce constraints provided by inclusive muon flux measurements into the calculations of lepton fluxes provided by the MCEq code to obtain a new atmospheric neutrino flux prediction.