In context, Mr. Darcy is replying to Miss Bingley, who has just accused Elizabeth Bennet of employing a “very mean art”:
“Elizabeth Bennet,” said Miss Bingley, when the door was closed on her, “is one of those young ladies who seek to recommend themselves to the other sex by undervaluing their own; and with many men, I dare say, it succeeds. But, in my opinion, it is a paltry device, a very mean art.”
Jane Austen (1813). Pride and Prejudice, chapter 8. Project Gutenberg.
By this “very mean art”, Miss Bingley means Elizabeth’s humorous self-deprecation, which she interprets as a device for attracting the attention of men. So when Mr Darcy replies to her saying
“there is a meanness in all the arts which ladies sometimes condescend to employ for captivation”
he intends this as a rebuke to Miss Bingley: that is, he can tell that she also has been employing arts to captivate men, and one of those arts is the deprecation of rivals like Elizabeth Bennet, but this will not work on him. After this rebuke is delivered, the narrator says:
Miss Bingley was not so entirely satisfied with this reply as to continue the subject.
This is humorous understatement (litotes): Miss Bingley is in fact quite upset, as she has been hoping to win Mr. Darcy for herself.