The title of this question is ambiguous as I couldn't think of anything better. What I'm trying to articulate is the thought of 'I didn't know at the time but do now'. Can this be expressed by saying 'Я не знал', or does it go deeper than that?
For instance, after going up to someone and asking about their cat, your friend says:
Его кошка умерла.
To which you respond,
Я не знал. (Meaning I didn't know at the time, but now I do)