Neutrino scattering on atomic systems at low-energy transfer is a powerful tool for searching the neutrino electromagnetic interactions. The regime of coherent elastic neutrino-atom scattering, i.e., when the atom recoils as a pointlike particle, can be effectively fulfilled in the case of tritium antineutrinos. We present theoretical calculations for coherent elastic neutrino-atom scattering processes on such targets as the H, $^2$H, $^3$He, and $^4$He atoms. We show how the atomic effects and neutrino electromagnetic properties, namely the neutrino millicharge and magnetic moment, may manifest themselves in the atomic-recoil spectra. Our results can be used in planning the experiments on coherent elastic neutrino-atom scattering (in particular, with superfluid He-4).