The psalm for Mass is not from Psalms, but rather from the book of Daniel: Daniel 3:52-56. Obviously that is not in the Coverdale Psalms. Moreover, it is not in the Coverdale Bible, of which the Psalms are as far as I know the only widely-used survival of that translation.
The reason it's not in the Coverdale Bible is probably known to those who are more biblically literate than I am: it's not in any Protestant translation, because it's only found in the Greek Septuagint, which Protestants don't consider to be authoritative. I only learned this because I thought I would see how it read in the King James, and couldn't figure out why in various online KJV sources Daniel 3 has only thirty verses.
Some Protestants, notably Anglicans, kept those and some other segments of Daniel as "apocrypha," which is why most Protestants probably don't know that marvelous passage known as the Song of the Three Young Men (or variants) in which Shadrach, Mesach, and Abednego (as I learned their names long ago) invoke a long list of things, beginning with "All ye works of the Lord," exhorting them to "praise and exalt him above all for ever." There is a great musical setting of it, more or less a chant as I recall (though it's been over forty years), that I heard once or twice when I was an Episcopalian.