This is where the Theology comes in. Generally speaking, we, as humans, are not worthy of being saved by God. The world with all of its problems is the inevitable result of our nature. We are selfish and sinful beings. There is no question about the fact that our selfishness is largely responsible for all of the pain in the world. Our sinful nature manifests itself in a number of ways. This includes things like lust, greed, and gluttony. The fact is we do not, in any circumstance, deserve salvation. We have no right to stand before God as we are not worthy of that gift. This is precisely why we need God's Grace. This came to us in the form of Jesus' sacrifice on the cross. Absent that sacrifice, we would all be condemned for our nature.
It is not hard to have this feeling. I have no doubt that to some degree we all feel this way, though we no doubt interpret it in different ways. We also have different ways of dealing with the situation, too.
During the era of the black plague, there used to be a group that would go around in public flogging themselves because the plague was thought to be a punishment from God for the sins of humanity. In reality, it was a bacterium that grew in stagnating waste water. A sewer system that prevented waste water build up stopped its spread. The point of the story is how we deal with these issues. Plague grew as a result of a specific set of conditions created by our own waste, and flogging one's self as punishment didn't solve anything. There is no point to inflicting punishment upon one's self because salvation comes through committing ourselves to a relationship with God through God's mercy and Christ's sacrifice on the Cross.
Bad things happen, good people do bad things, and the only plausible cause is that we are all fallibly human. The book of James suggests that we confront trials in order to bring us closer to God, that we suffer trials so that we may grow near to God by learning more about God. Repenting for Sin is a large part of this process. Being humble in the sight of God is more about admitting that you are a sinful being not worthy of God's grace, then enumerating those transgressions. At the same time, we shouldn't let these feelings of worthlessness prevent us from thinking that a meaningful relationship with God is impossible. If anything, this is just another diversion away from God. Micah put it best:
Do not rejoice over me, O my enemy. Though I fall I will rise; though I dwell in darkness, the Lord is a light for me. I will bear the indignation of the Lord because I have sinned against Him, until He pleads my case and executes justice for me. He will bring me out to the light, and I will see His righteousness.
Micah 7:8-9. This reinforces the idea that though we sin and are sinful, there is salvation, and that we should not permit thoughts of worthlessness or inadequacy to permeate our feelings in a way that detracts from God since that is not what we have been promised by God's salvation through Christ's sacrifice.
After all of this theology, we get to the grand point. These feelings of worthlessness relate directly to our walk with God. Whether we let ourselves be consumed by feelings of self hate and loathing, and stray back into sin for satisfaction, or come to rely on God and pursue knowing more about God, is a determination ultimately up to us as individuals. I posit that the appropriate way here is to be humble before God, take the time we need, and avoid being the soil and seed choked by the vines and thorns of busyness that life in the modern western world forces upon us.