Coming from another reserved person, make sure that you present the reasonings for why you should have a raise in terms of data; i.e., "I have saved us $X dollars per year by...", "I have performed very well which has resulted in customer queues dropping by X.X minutes", "Here are several written compliments from customers about my work", "With my education and experience the average salary for this position is" and so on.
Play to your strengths, which is not being a quiet, shy type, but rather by being analytical (or such that often applies to introverts). You can still negotiate with charismatic extroverts because it is hard to dismiss logical data.
The real issue, for me at least, is staying on track with an extrovert because it is common to be overwhelmed and side-tracked, which is a way of avoiding your talking points. I find it very important to remain composed, and keep reminding the other person that you would like to get back on track regarding your work performance, as well as your suggested raise.
But to answer your question regarding how not to get dismissed in negotiations: it is just as much the other parties' job to negotiate a raise (or plan, idea, etc.) as it is yours, so keep that in mind and do not be disheartened when (most likely) he shuts down your proposal and offers little-to-nothing. If you deserve a raise then you should have the data to back it up, so make sure to use it to find a middle-ground which both of you can agree on. It should be discussion rather than a yes/no.
There are also, of course situations where the other party refuses to back down, where no matter what you say, do or show will make him change his mind, and in those cases it is better to shop around for other oppertunities.