Here's what Atomica (soon to become Gurunet again, apparently) has:
dep·re·cate (dĕp'rĭ-kāt')
tr.v., -cat·ed, -cat·ing, -cates.
To express disapproval of; deplore.
To belittle; depreciate.
[Latin dēprecārī, dēprecāt-, to ward off by prayer : dē-, de- + precārī, to pray.]

dep're·cat'ing·ly adv.
dep're·ca'tion n.
dep're·ca'tor n.
USAGE NOTE The first and fully accepted meaning of deprecate is “to express disapproval of.” But the word has steadily encroached on the meaning of depreciate. It is now used, almost to the exclusion of depreciate, in the sense “to belittle or mildly disparage,” as in He deprecated his own contribution. In an earlier survey, this newer sense was approved by a majority of the Usage Panel.

From the quote, I can't think that Nicias is disapproving of or deploring his people, nor warding them off by prayer. I was thinking that, had Dryden added 'himself' after deprecating, it would read a little better. But grovelling gets the idea across pretty clearly, without the extra word.
What is meaning of in fine, please?