Ethnocentrism would have a very negative impact on the success of an international manager. Ethnocentrism is the general belief that your own ethnic group is better than other groups. An international manager would be badly hurt by this belief because they would tend to look down to some extent on people from other cultures or ethnic groups. They would have a hard time getting along with such people because their attitudes would probably end up being communicated in one way or another. They would have a hard time accepting feedback or taking comments from people of other ethnicities because they would not really take those people seriously.
In other words, an ethnocentric international manager would not work at all well with people from other ethnic groups. Since an international manager must by definition work with such people, an ethnocentric manager would not be likely to succeed.