What did Jesus mean by that statement? Is that meaning the righteousness of Christ given to believers?
Yes.
Spot on.
Even if we lived our lives and did our best to be justified under the law, our righteousness is not enough.
(the end of romans 9 and start of 10 in my opinion words this very clearly)
What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.
Brethren, my heart's desire and prayer to God for Israel is, that they might be saved.
2 For I bear them record that they have a zeal of God, but not according to knowledge.
3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
4 For Christ is the end of the law for righteousness to every one that believeth.
5 For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them.
6 But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down from above
7 Or, Who shall descend into the deep? (that is, to bring up Christ again from the dead.)
8 But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word of faith, which we preach;
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
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