Does the Bible teach that we have only one book of inspired praise and that is the book of Psalms and therefore nothing of mere human composition is ever to be sung? I do not believe that it does. I don't believe that the Scriptures nor Church History agrees with the exclusive Psalmist position.
Here are a over a dozen reasons for believing so.
It is the premise of exclusive psalmists that these terms refer to the divisions of the Psalter in the Greek Septuagint version of the Old Testament.
However, the meaning of a Bible word is to be ascertained by its usage in the inspired Scriptures and not merely by its usage in a translation of the Scriptures. Keeping this principle in view the word 'Psalms' in the New Testament is used in a far wider manner than the 150 Psalms of David. It refers to a whole section of the Old Testament, Luke 24:44 And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.