Actually the Church did not "add" those books at all...let alone at the Council of Trent.

The short answer:
The books you call the Apocrypha (we call them Deuterocanonical) were included in the Jewish Scripture as early as the 3rd century BC.  About that time the Jews wanted - and had translated - Scripture in their own language, which was Greek.  This greek translation was called the Septuagint (LXX), and contained the Deuterocanonical books.

The LXX was clearly in use in apostolic times, as evidenced by the quotes of it in the New Testament: about 70% of NT quotes of Scripture were quotes from the LXX.

It was not until the latter part of the 1st century AD that the Jews rejected the Deuterocanonical books - many believe due to an effort to separate themselves from the Christians.

The early church accepted them:
"The sub-Apostolic writings of Clement, Polycarp, the author of the Epistle of Barnabas, of the pseudo-Clementine homilies, and the "Shepherd" of Hermas, contain implicit quotations from or allusions to all the deuterocanonicals except Baruch (which anciently was often united with Jeremias) and I Machabees and the additions to David. No unfavourable argument can be drawn from the loose, implicit character of these citations, since these Apostolic Fathers quote the protocanonical Scriptures in precisely the same manner." [source]

For a fuller explanation of the Canon of the Old Testament, see here...expecially the section a bit more than halfway down called B. THE CANON OF THE OLD TESTAMENT IN THE CHURCH OF THE FIRST THREE CENTURIES