Everyone thinks in different ways, so there will always be personality clashes. It is a fact of life.
However, the number one way to avoid, or lessen, management problems is effective communication. Lack of communication causes a good percentage of the problems in organizations. It leads to frustration, irritation, and stress. Effective communication will get everyone on board and make them feel like they are part of the team.
Communication is so important that a recent Inc. Magazine article ranked lack of communicating a vision as one of the top 7 reasons employees quit their job (https://www.inc.com/lolly-daskal/7-reasons-the-best-employees-quit-even-when-they-like-their-job.html). Having happy, productive employees is another way to lower management problems, so communication across the organization is vitally important.
As introverts, we tend to avoid face to face interaction, especially when there is possible conflict. But there are ways to lessen the trepidation of such encounters: practice. Find a person you are comfortable with and practice the interaction, and here is your tip: Practice a Positive Outcome. Yes, practice communicating a positive outcome. Put your introvert influence to work, and you will do amazingly well.