We should read functionalism as denying that mental properties like being in pain are neural properties. Rather, there are neural properties that realize mental properties. Thus, the property P of being in pain is the property of being an x that has a property N such that FP(x,N), where FP(x,N) is a predicate that says that N is a property exemplified by x that plays the pain role in x. The property N is a realizer of the pain property P in x. The materialist functionalist then says that the realizers of our mental properties are all neural properties.
The causal theory of content, in a functionalist context, identifies the content of a fundamental perception as the relevant cause of the realizer of that perception. Thus, perceptions whose realizers are typically caused by horses have horses as their intentional content.
Now among our perceptions, there are introspective perceptions of our own mental states. When I have pain, I often perceive that I have pain, and sometimes when I am puzzled, I perceive that I am puzzled. But now we have a problem. For the most plausible story compatible with the above about how we form introspective perceptions is that they are caused by the states that realize the mental states that the perceptions are of. Thus, if N is the neural state that realizes my pain, my perception of my being in pain is caused by N. But by the causal theory of content, that perception's content, then, is the neural state N. In other words, instead of perceiving that I am in pain, I perceive that I am in such-and-such a neural state. Yet although the neural state realizes the pain, it is distinct from the pain. The pain is a second-order property, while the neural state is a first-order property.
So, it seems that the causal theory of content plus functionalism predicts that our introspective awareness is neural states rather than of the mental states the the neural states realize. But surely our introspective awareness is of mental states.
But perhaps we can extend the causal theory of content to an explanatory theory of content. And while the second-order state of being in pain perhaps doesn't cause the realizer of the introspective awareness of the pain, nonetheless the state of being in pain explains either the realizer of the introspective awareness or the introspective awareness (a functional state) itself.
But I think this is implausible. For consider extra-mental functional stuff. Thus, green rectangles realize money. As children, we first see the green rectangles as such. Later we see these green rectangles as caught up in a great functional systems, and we come to see not just green rectangles but the money they realize. It is the physical stuff that is the first object of perception, and the perception of functional stuff is built on that. By analogy, then, we might predict that if functionalism and the causal theory of content are correct, then before children introspect to their pain, they introspect to their neural states. But that is deeply implausible. On the contrary, it is the introspection of the mental, not the neural, states that seems to come first, both chronologically and phenomenologically.