But for what it's worth, the nearest thing to a statement of this idea in the actual Bible, which comes in the Letter to the Romans, says this:

I've found a few other passages that seem to have a bearing on this question.

Luke 12:47-48 states:

47 “The servant who knows what his master wants but is not ready, or who does not do what the master wants, will be beaten with many blows! 48 But the servant who does not know what his master wants and does things that should be punished will be beaten with few blows. From everyone who has been given much, much will be demanded. And from the one trusted with much, much more will be expected.

...which implies that, while there is a punishment for sin committed in ignorance, it is far less than that for sin committed knowingly.

(Proverbs 24:12 also seems relevant; and there's a lot of probably-at-least-slightly relevant passages linked from here).