What was "the principle of which we were ashamed" in the writing of the constitution?

Slavery--the word "slave" or "slavery" is never explicitly stated in the Constitution.

The statement referred to the three-fifths compromise regarding representation for the House of Representation. The South demanded their slaves be counted as persons but not be regarded as persons or even freed in the law. The compromise counted "other persons" as 3/5 a person when counting for representation as opposed to a whole when counting whites. Some of the Representatives from the North felt this was a moral error and one the US should be ashamed.