Yes but why the need to put a period for something which is not a full sentence?! I thought periods are only used for full sentences! Can you please give me an example of what you mean to clarify?
It seems like every time we're about the end our meeting, she always say, "Oh, wait, one more thing." No matter what you ask him for, his answer is always "probably not."
The part being quoted isn't a full sentence. However, in the US, the period goes inside the quote anyway. In other parts of the world, the period (full stop) would go outside of the quotes.