The structural and magnetic interactions in stoichiometric (Mn₃SnC), carbon deficient (Mn₃SnC_0.8) and tin deficient (Mn₃Sn_0.85C) antiperovskite compounds are studied using X-ray absorption fine structure spectroscopy and neutron diffraction. The study confirms the presence of local structural distortions only around Mn atoms in the antiperovskite compounds irrespective of their stoichiometry. The distortions in the Mn₆C octahedra are such that only Mn atoms are displaced from their crystallographic positions resulting in long and short Mn–Mn bonds. These long and short Mn–Mn bonds are responsible for the presence of ferromagnetic and antiferromagnetic moments on Mn atoms. The C deficiency at the center of the octahedra increases the strain on the Mn₆C octahedra and results in a wide variation of Mn–Mn bond distances as a function of temperature and large hysteresis in magnetic properties. On the other hand, Sn deficiency tends to relax strain by giving more space for the octahedra to distort leading to temperature independent Mn–Mn bond distances.