No, the problem was Nintendo, and their restrictions on third party publishers that said that if they publish games for the NES, they cannot publish for any other system. That is why apart from Activision and Parker Bros., every SMS game in North America was published by Sega. Of course, Nintendo's tactics were eventually found to be illegal, which is why the Genesis had fantastic 3rd party support.
None of this applied in Europe, however, where Sega had full third party support, and easily trounced the NES over there.