What's meant here by "Don't mention it"?

Question

In "The Quick One" by G. K. Chesterton, Father Brown was talking to his friend, saying:

Didn’t you see how that old man, with the heart of a lion, stood up and forgave his enemy as only fighters can forgive? He jolly well did do what that temperance lecturer talked about; he set an example to us Christians and was a model of Christianity. And when there is foul and secret murder of a man like that — then I do think it matters, matters so much that even the modern machinery of police will be a thing that any respectable person may make use of ... Oh, don’t mention it. And so, for once in a way, I really do want to make use of you.’

I found, in almost every dictionary, that "don't mention it" is "A polite expression used to indicate that an apology or an expression of thanks is not necessary."

But that doesn't make sense in this context, so I guess that he mean "shut up my mouth" because he praised himself as a respectable man, doesn't he?

Answer 1

I do not know of any explicit statement of what was meant there, but my interpretation of it was that he was being met by a gesture of appreciation by Inspector Greenwood for his inspiring speech, and was trying to fend off that implied praise. My impression was that Father Brown started making this grand speech about Raggley being the best sort of Christians, and that the Inspector may have made some gesture of approval, something like quiet applause, nodding, or the raising of a hand as if as a toast, prompting Father Brown to beg off the praise. Of course, no such gesture is described, but that is the distinct impression I got in reading the passage.

I could also see a reasonable interpretation for that he was cutting himself off either because he felt that he was going off-topic, or even lapsing into preaching. Or, as you say, because he'd accidentally labeled himself a "respectable person". In that case, the "don't mention it" is a little closer to saying "forget it".