I checked my Funk & Wagnalls, then I checked a couple of on-line sources. The closest I could come was this:
With the permission of; with deference to. Used to express polite or ironically polite disagreement: I have not, pace my detractors, entered into any secret negotiations. (AHD)
It seems rather quaint, and it does not mean sorry. As you can imagine, I have never heard the word used to mean sorry. Sorry.