It's not as simple as that. This is from the newadvent website:
The Council of Trent (Sess. XIII, cap. iv; can. ii) not only accepted as an inheritance of faith the truth contained in the idea, but authoritatively confirmed the
"aptitude of the term" to express most strikingly the legitimately developed doctrinal concept.
http://www.newadvent.org/cathen/05573a.htm#3
So they merely stated that Transubstantiation was an acceptable term to describe the mystery of the eucharist. Mostly in response to protestant attacks on it. Again, this has to do with the western mindset's need to rationalize and explain everything. The East remain prefer to say its a mystery thats beyond trying to explain so there's no use in trying. But both believe in the real presence.
Interestingly the catechism of the Catholic Church presents it back in its more mystical form:
1357 We carry out this command of the Lord by celebrating the memorial of his sacrifice. In so doing, we offer to the Father what he has himself given us: the gifts of his creation, bread and wine which, by the power of the Holy Spirit and by the words of Christ, have become the body and blood of Christ. Christ is thus really and mysteriously made present.
1358 We must therefore consider the Eucharist as:
- thanksgiving and praise to the Father;
- the sacrificial memorial of Christ and his Body;
- the presence of Christ by the power of his word and of his Spirit.