Density functional theory calculations were performed to study the structure and magnetic properties of bcc (α) and fcc (γ) Fe with 3 at.% carbon and manganese impurities. We find that all bcc-based Fe, Fe-C and Fe-Mn-C phases exhibit a ferromagnetic (FM) ground state, while the antiferromagnetic double-layer (AFMD) state is lowest in energy within the collinear spin approach in fcc Fe, Fe-C and Fe-Mn-C phases. However, the carbon and manganese impurities affect the local magnetic interactions significantly. The states with opposite manganese magnetic moments are quasi-degenerate in bcc Fe-Mn alloy, whereas octa-site carbon stabilizes ferromagnetic coupling of the nearest manganese atom with the Fe host. We demonstrate that the antiferromagnetic (AFM) fcc Fe-C and Fe-Mn-C alloys are intrinsically inhomogeneous magnetic systems. Carbon frustrates the local magnetic order by reorientation of magnetic moments of the nearest Mn and Fe atoms, and favors their ferromagnetic coupling. The competition between ferromagnetic and antiferromagnetic Fe-Fe and Fe-Mn interactions and the local magnetovolume instability near carbon may give rise to the spin-glass-like regions observed in austenitic Fe-Mn-C alloys.