For the record, as a Protestant, I believe God effects salvation through His Sacraments too.
So do many Protestants.
And both Catholics and Protestants believe salvation is a supernatural miracle from God, God's gift to us, by His grace and His loving action toward us.
The fundamental difference is over Justification and Sanctification, Catholics believe the two are coterminous, whereas there is a very sharp distinction between the two in the theology of the Reformation. Additionally, the role of human action in Justification is different: In Catholic theology Justification is a process which man is an active participant in through cooperation with God's grace through faith evident and active in a life dedicated to obedience and love toward God (what we usually call "good works") and thus human will is a partner in God's gracious and loving act to justify us and save us. In the historic teaching of Protestantism, Justification is something wholly apart from human cooperation, will or effort but a free and unmerited act of God by grace acting alone through faith alone (itself a gift from God apart from the work or effort or will of man), and thus man is unable to cooperate or become an active agent in this divine act of God which He does freely by His own will through the means He has established (namely, His Word and Sacraments).
Fundamentally, as far as Justification is concerned, the usual Evangelical model of "accepting Christ" is foreign to the historic Protestant position and is, in fact, closer to the Catholic model insofar as it makes man an active participant and cooperator with God in Justification by saying that man must exercise his will.
That is to say, for example, that coming from a Lutheran position, the standard Evangelical model and the Catholic model are, substantially not very different at all. The heart of the theology of the Reformation in regard to Justification has as much a problem with the standard Evangelical model as with the Catholic model. And, yes, that was at the heart of the Reformation, everything else is--more or less--completely peripheral.
That said, while there are most definitely significant disagreements between Catholics and Protestants over Justification--they are not minor differences that we can simply brush aside as though they aren't vitally important--the level of anti-Catholic sentiment that some ill-informed or sometimes just plain malicious Protestants have, the fact of the matter is that Roman Catholics and Protestants are both Christians in the full sense of the term. We confess the same God, the same Christ, the same Creed and share in the same Baptism which unites us in common to our same Lord Jesus.
-CryptoLutheran