One cannot be justified without being regenerated. Justification is a legal standing before God and is only obtained through faith in the person and work of Christ. His work on the cross as our substitute, satisfied God's justice against our sin. Therefore we are declared just by virtue of Christ's righteousness.
And one cannot see or enter the kingdom of God unless they are born again (John 3)---regenerated. Regeneration results in the work of Christ being applied to the person---justification.
Seeing the kingdom is an issue for those in Judaism who could not, actually.
"Regeneration results in the work being applied..."? I don't follow this. The debt of sin and the dirt of doing it are two very different things, except where the guilt of the debt makes us try to clear the debt religiously. You could say the debt of sin otherwise is a totally different force.
Church songs have preserved the difference of debt and stain:
Rock of Ages:
"Be for me a double cure; save me from sin's guilt and power."
Oh For A Thousand Tongues:
"He breaks the pow’r of canceled sin,".
Nothing But the Blood Of Jesus:...
There is a link between cancelation and power, like in Rom 6: why would we do what brought us death before? Ie, the gift of justification is so sweet that why go on in sinful actions?
In "Nothing" most of the verses deal with the debt, but the rest and chorus is about being washed, overcoming. Here are the verbs that match debt:
pardon, plea, atone, (no) merit, my righteousness. If you need further financial analogy, justification is like having a life insurance policy, regeneration is like making the monthly payment. That monthly payment is not a debt (most policies value is far above what is paid in), but it is a participation that
admits it is necessary when there are no other resources.
I do not find a mystical blood-power in the NT. It is for debt, for atonement. Sometimes regeneration is a task, a battle that we are to master, to work out on our own.
Since 'applying' Christ's righteousness has to do with debt, I do not accept the wording 'regeneration applies the work of Christ to the person.' Cause and effect is the other way around. Justification results in new thoughts, hopes, inspiration.