What it reminds me the most of is Harry's discussion with Hermione about the need for heroic responsibility - about always shouldering the responsibility for any final outcome of events, instead of thinking that your job is done when you, say, go to Professor McGonagall and tell her to do something about it.

My guess(though I wouldn't assign a very high probability to this) is that it will be uttered by Harry while he's away from anyone he considers to be sane or responsible(like, say, Quirrell) and he fails to prevent something tragic from happening. A more specific hypothesis: Quirrell's identity is revealed by him doing something unspeakably evil and Harry blames himself for not piercing the disguise earlier.