The effect of strain due to lattice mismatch and of ferromagnetic exchange field on superconductivity ͑SC͒ in NbN-CoPt bilayers is investigated. Two different bilayer systems with reversed deposition sequence are grown on MgO ͑001͒ single crystals. While robust superconductivity with high critical temperature ͑T c Ϸ 15.3 K͒ and narrow transition width ͑⌬T c Ϸ 0.4 K͒ is seen in two types of CoPt-NbN / MgO heterostructures where the magnetic anisotropy of CoPt is in plane in one case and out of plane in the other, the NbN-CoPt/ MgO system shows markedly suppressed SC response. The reduced SC order parameter of this system, which manifests itself in T c , temperature dependence of critical current density J c ͑T͒, and angular ͑͒ variation of flux-flow resistivity f , is shown to be a signature of the structure of NbN film and not a result of the exchange field of CoPt. The f ͑H , T , ͒ data further suggest that the domain walls in the CoPt film are of the Néel type and hence do not cause any flux in the superconducting layer. A small but distinct increase in the low-field critical current of the CoPt-NbN couple is seen when the magnetic layer has perpendicular anisotropy.