Deut. 25:2-3: If the guilty man deserves to be beaten, the judge shall make him lie down and have him flogged in his presence with the number of lashes his crime deserves, but he must not give him more than forty lashes. If he is flogged more than that, your brother will be degraded in your eyes (NIV).
Jewish law provided that punishment should fit the crime, but also that it not be too severe. A penalty that was too light minimized the crime, but a punishment that was too severe degraded and humiliated the person. Penalties were required to be "just".
This is the law of our country also, according to the Eight Amendment. Should the principles be any less effective in our discipline of our kids? Sometimes we overdo our discipline. Maybe we had a bad day or the offense was one that just got under our skin.
Regardless, when we discipline our kids too harshly, we have violated this principle. The best response is to demonstrate what a person of integrity does when they have wronged another—apologize specifically and ask forgiveness. That does not mean there is no consequence for the original offense. It only means we recognize we have also offended and that we are not above the rules.