What is to explain? The passage says everything the Catholic Church teaches: that sin is redeemed by the blood of Christ, in which we have faith (hm...); that grace alone justifies us given us freely without merit on our part. You did not include the remainder of the passage but had you read a couple verses down you would have seen that the thrust here is with the impossiblity of salvation by "works of the law", as the Jews believed. The passage does not say that we are saved by faith alone, and we do not teach that we are saved by works alone. We believe what St. Paul teaches. You don't: you add your own spin to his belief and in other places you ingore the Gospel altogether. You, for example, do not believe that His Blood is present in the Eucharist even though that belief is cited here as saving faith.
Let's look at that context:
Romans 3:20-31
Therefore no one will be declared righteous in God’s sight by the works of the law; rather, through the law we become conscious of our sin. But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify. This righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, for all have sinned and fall short of the glory of God, and all are justified freely by his grace through the redemption that came by Christ Jesus. God presented Christ as a sacrifice of atonement, through the shedding of his blood—to be received by faith. He did this to demonstrate his righteousness, because in his forbearance he had left the sins committed beforehand unpunished— he did it to demonstrate his righteousness at the present time, so as to be just and the one who justifies those who have faith in Jesus. Where, then, is boasting? It is excluded. Because of what law? The law that requires works? No, because of the law that requires faith. For we maintain that a person is justified by faith apart from the works of the law. Or is God the God of Jews only? Is he not the God of Gentiles too? Yes, of Gentiles too, since there is only one God, who will justify the circumcised by faith and the uncircumcised through that same faith. Do we, then, nullify the law by this faith? Not at all! Rather, we uphold the law.
So you see, I hope, that we are justified by faith. There is a Law of Works (which you seem to fancy), and there is a Law of Faith. We ARE saved by faith alone, and it is your "spin", or the spin you have heard all your life, rather, that insults and ignores the true Gospel.
The idea that this passage gives credence to His Blood is present in the Eucharist is nowhere to be found here much less that belief in that idea is required for "saving faith". When we trust in the sacrifice of Jesus Christ on the cross for our sins, we BY FAITH receive him and this act of genuine faith is what puts into place the redemption of our souls - we do not have to continuously receive him through a reinactment of the sacrifice of the Mass in order to be saved. But go right ahead and believe that, I know my words will never convince anyone, it is only the Holy Spirit with each individual heart who can do that.