Paul said that God was not at fault for the Jews not believing in Messiah. He ended by calling them a disobedient and obstinate people. It was their own fault. Yet, before we begin to think that Gentiles are some how better (they aren't), Paul continued to teach on God's plan for the Jews.
Romans 11:1-6 (KJV)
I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel, saying,
Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.
But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
Even so then at this present time also there is a remnant according to the election of grace.
And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.
In verse 1 Paul again used a leading question to shape his argument. "Has God cast away his people?" Paul answered negatively, "God forbid!" Paul then used himself as an example of how God had not cast the Jews aside. Paul was a Jew, a descendant of Abraham, and a member of the tribe of Benjamin.
God had not cast away the Jewish people which He had foreknown (verse 2). Paul then used Elijah as his second example. After Elijah had confronted the prophets of Baal, he fled and complained that he alone was left of all the prophets of God (verse 3). Yet, this was not true (verse 4). God had reserved seven thousand men who had not turned to Baal. God had preserved a remnant.
In verse 5 Paul affirmed that during his own day, there was still a Jewish remnant of believers in Messiah, that were saved by grace.
While much of Christianity today has also decided that God is through with Israel (Replacement Theology) and that the Church has replaced her, Paul's words and examples show that there will always be a remnant of Jews that responds to God's call. There will be more as chapter 11 continues.
Then in verse 6 Paul returned to one of his major arguments, that since the Jews' salvation was by grace, it was not of works, otherwise grace would not be grace, but payment of a debt. And if salvation came by works, it was not of grace. Then works would not be the loving and thankful result of salvation, but the striving for something that was unattainable. Again, Paul stressed that, as always, salvation came by grace!