Note: I don't quite completely understand your question and would appreciate if you added some reference text to further elucidate your question (which may help me to correct my answer as well, if required).
I think the key distinction between intrinsic and extrinsic motivation is not the awareness of the motive, but the locus of origin of the motive.
We are very much aware of intrinsic motives. For example: Hunger- Going without food for a long time makes us hungry, a state we are aware of, and we consume food. The act of consuming food when hungry is intrinsically motivated, and emerges from within us, without the effect of any external agent.
As you have mentioned, we are also aware of our extrinsic motives, for example, motivation to work a 9-to-5 job to earn money to buy food which satiates hunger, a primary need.
References:
Psychology, Ciccarelli, fourth edition.
http://ccdf.ca/ccdf/NewCoach/english/ccoachb/issue_b1c_basics.htm