I wish I could claim ignorance on the question, resulting from having never received any. Failing that, I wish I could say I have mastered how to handle it. The hard truth is that I receive plenty of criticism. Some of it I deserve. Some of it I don’t. All of it is hard to deal with. What follows then isn’t necessarily what I do, but is instead what I think we all ought to do.
First, fight the temptation to assume the criticism is undeserved. If “people” are bad enough to make all manner of false accusations, and they are, and you are a “people, don’t you think “people” including you might also be bad enough to be blind to their own faults? I have faults, plenty of them. Though I may try to conceal them, I fail at that too. So it may just well may be that the ones I am being accused of are the ones I am guilty of.
Second, forget about how the criticism was delivered, and by whom. Because we are sinners we seek to excuse ourselves, justify ourselves, on the basis of the sins of others. I’ve never met anyone who confessed to being rightly fired from a job. I have met plenty who complained, “I’m not upset that they fired me. It’s the way they did it that bothers me.” Properly translated what they really mean is “I’m upset that they fired me.” Remember that God delivered some fairly compelling criticism through an ass once, and unlike flooding the world, He did not promise never to do it again.
Third, even if the motive behind the criticism is the devil trying to discourage you, he is unlikely to do so by making an accusation that has no resemblance to the truth. The devil would never accuse me of having too high a view of my height. The accusation is laughable. He might, however, accuse me of having too high a view of myself. That one sticks.
Fourth, therefore seek to learn from the criticism. Take the time, in a calm and peaceful manner, to explore that truth the criticism might touch on that is a weakness. Don’t diminish, rationalize or deflect. Do seek to learn the most gentle means of correcting others. Do learn your own blind spots.
Fifth, repent and believe the gospel. Know that your heavenly Father knows things about you that are far worse than whatever you are being criticized for. Know that He knows things about you that even you don’t know. He understands the fullness of how far short we all fall. And He calls us to repent. Repent to Him. Repent to your critics. Repent to those you have disappointed. Do it freely and fully, because in believing the gospel we know that the Father who knows us fully loves us fully. Not because we are better than our critics think. Not because we are better than we think. Not because we are better than He thinks. But because Jesus is better, and we are in Him. Our believing of this good news ought not to be so swift that we forget to repent. Our repentance, however, should never overshadow the certainty of His love. Instead it pushes us to the certainty of His forgiveness. It’s hard to stay down in the dumps when you remember how much He loves you.