I am not implying Darcy owes Lizzy an apology. I sincerely believe he does. I agree with Karen 2L. (:D) You of course need not agree but here is why I think he does:

"Oh! she is the most beautiful creature I ever beheld! But there is one of her sisters sitting down just behind you, who is very pretty, and I dare say very agreeable. Do let me ask my partner to introduce you." (Chapter 3)

In Chapter 3, Bingley points out that Lizzy is sitting down just behind Darcy; he then turns around and meets Lizzy’s eye before coldly responding to his friend that she is tolerable… and etc. As Arnie quite rightly points out above Darcy is not a social ignoramus and I would further add not any kind of ignoramus at all. IMO he should know that Lizzy can hear him because first, she is just sitting behind him and second, he just assured her attention would be fixed on him by meeting her eye and three, despite her proximity to him makes no effort to lower his voice so only he and Bingley can hear his response. Although turning his back on Lizzy breaks eye contact it has never been known to turn ears off. Since Darcy is not above eavesdropping himself why should I reasonably believe Darcy thinks addressing someone personally is a means to assure the privacy of his conservation? ;D

If you like to imagine that Darcy was only speaking in a normal conversationally pitched voice then he still cannot be excused from understanding Lizzy might overhear his response. If he is speaking normally then she is indeed sitting just behind him—unless of course you attribute Super-hearing as one of Lizzy’s particular charms as they are after all in a crowded insupportable noisy assembly. She must hear him over the general noise and movement of a crowd, the noise of multiple conservations and the noise of music, laughter and people dancing as well as other activities in the background such as card games and servants bustling about. ;D

Darcy insults Lizzy’s appearance and consequence based on nothing but his preconceived ideas of the type of lady he thought she was. Arnie was asserting that Darcy felt bad for what he said about Lizzy and although I do not agree with Arnie, if that is indeed the case then he owes her an apology—for saying it, because she heard it and also for disparaging her to his friends. If Darcy was too self-absorbed or stupid at that moment to realize Lizzy was close enough to overhear him then he still owes her an apology for the wrong he has done to her if not for his intent. His intent does not matter IMO and it has never been the basis of why I believe he owes Lizzy an apology. I believe that Darcy just did not care if Lizzy overheard him because he believed she was beneath him and not worth the attention of dancing with or taking precautions so she would not overhear his response. ;D