No. :)
Local Councils are binding to local Churches.The Council of Carthage was binding to the Western (Latin) Church because it was accepted by the Bishop of Rome (Patriarch of the West). Thus the canon was set in the West by the 5th century. The Council of Trent merely reiterated the canon of the Council of Carthage centuries later.
The Council of Carthage was but one of many local African Councils. It was, in no way, binding on the entire Church.
Catholic Encyclopedia - The 21 Ecumenical Councils
The most explicit definition of the Catholic Canon is that given by the Council of Trent , Session IV, 1546. For the Old Testament its catalogue reads as follows:
The five books of Moses (Genesis, Exodus, Leviticus, Numbers, Deuteronomy), Josue, Judges ,Ruth, the four books of Kings, two of Paralipomenon, the first and second of Esdras (which latter is called Nehemias), Tobias, Judith, Esther, Job, the Davidic Psalter (in number one hundred and fifty Psalms), Proverbs, Ecclesiastes, the Canticle of Canticles, Wisdom, Ecclesiasticus, Isaias, Jeremias, with Baruch, Ezechiel, Daniel, the twelve minor Prophets (Osee, Joel, Amos, Abdias, Jonas, Micheas, Nahum, Habacuc , Sophonias, Aggeus, Zacharias, Malachias), two books of Machabees, the first and second.
Catholic Encyclopedia - The canon of the Old Testament in the Catholic Church