I'd be interested to know if you are generally quiet around people. Do you normally prefer to be reserved?. If so, the reason you feel awkward and look uninterested is probably because you are very self conscious and don't like to be observed by too many people, nor have the energy or desire to take control of conversations in these situations because you are so distracted.
Personally, I don't think that is a bad thing. Such people become the writers, scientists, and poets of this world. However, if you really desire to speak with others [obviously you would like to date some] you need to teach yourslef to focus on a conversation. That is, take your awareness of others out of the picture and 'get into' the conversation at hand, much like if you were into writing a book. If it is interesting, get involved in the conversation and interact focussing only on the other person. Society often labels less naturally 'social' people as socially inept but thats not true, most of us can have one-on-one conversations with the best of them, if not even better because of our ability to focus rather than mingle. Of course if the conversation is predictable and boring, switch on the bored look
It's just a matter of exacerbating what you are best at, and blocking out some messages society can give you.
Oliver