"Experience" is a term used in a number of different ways in English and, therefore, somewhat vague in definition. As with many such terms it is easier to use - and to understand someone who uses it - than it is to define. The dictionary is not of much help here. It is best to turn to how the word functions in normal usage. We talk of "building up experience," or of our actions and ideas being "based on experience," or of having had "a strange experience," or of people being "experienced" or "inexperienced," and so on.
We might say that "experience" is "whatever is going on right now." And in this sense consciousness or memory are not essential. We don't say, for instance, that if someone has forgotten something that they never experienced it. Similarly, we can talk about the meaning of an experience changing when we find out new information about what was "really" going on or when we have a different perspective to it. However, we tend to speak of "how I experienced it then" and "how I experience it now," without suggesting that we did not have the first experience. We may now have decided we were mistaken in what we thought was going, that we experienced it as if it were one way and now realize it was another, but both were experiences. Therefore, awareness and conscious apprehension are not necessary requirements for using the term "experience" (though there may be disciplines that use the term technically and define it in terms of conscious awareness).
What we are coming to (and, surprise, surprise, it is in accord with our own usage) is that "experience" is, by analogy with fish, the medium in which we humans float and have our being. In some ways it is an interface phenomenon, but it gets sticky when you try to pin down what it is the interface between. While we might more often use the term to refer to things we consider to be going on in the external world, we have no reservation about speaking of internal experiences. For instance, our experiences of physical pain or pleasure are one whole category of internal experiences. Our experiences of emotional pain or pleasure are another. Perhaps all that can be said is that experience is the interface between "self" and the "external world," in other words, between two conceptual entities that are problematic and groundless.