One-loop radiative corrections introduce the dependence on the neutrino flavor in CEvNS. To consistently account for radiative corrections, we present the effective field theory of neutrino-lepton and neutrino-quark interactions, embed quarks into nucleons and nucleons into nuclei. We calculate CEvNS cross sections and flavor asymmetries on the spin-0 nucleus at energies below 100 MeV including all kinematic dependence of radiative corrections. We provide a complete error budget accounting for uncertainties at nuclear, nucleon, hadronic and quark levels, and add a perturbative error in quadrature. At 20-100 MeV energies, the uncertainty is limited by the knowledge of neutron distribution inside nuclei. Going to lower energies, hadronic contributions become the dominant source of uncertainty. Our precise predictions can be useful for electroweak measurements at low energies, studies of standard and non-standard neutrino interactions as well as for monitoring of nuclear facilities and precise knowledge of neutrino floor.