This is a response to a question posed by a friend at work. If you find this hard to understand, that's because it's lacking the context. Please just move on.
As a Christian, I no longer measure my self-worth by human standard because it's pointless. I used to measure myself against other people to see if I was any better than them. It wasn't hard to find someone who seemed morally worse than I was, which made me feel somewhat good about myself. But then I met Jesus. Then I understood that
1) I was morally bankrupt. In Jesus, I saw how high God's standard was.
2) comparing my moral behavior with others didn't do any good to me since God knew my heart and trying to soothe my conscience through comparing myself to other people itself was deemed evil in God's eyes.
3) even if measuring my self worth against other people was an acceptable thing, I no longer see the need of it since God says that I'm more precious than I could ever imagine myself to be and that I am pure and blameless in His sight through the blood of Jesus.
4) since God has declared I am of great worth, it's just not satisfying for me to get a sense of self worth by comparing myself to others anymore. Why go after the ignorant's opinion about me when the perfect and all-knowing Judge tells me who I am?
5) going to God for His approval instead of getting my own sense of self worth liberates me from judging others. I'm so bad only God can save me. So how can I look down on other people? I still make this mistake time to time but the gospel foundation reminds me that I can no longer boast about myself.
So in a sense, I kind of accept my own limits as you suggest, but in a different way. I accept the fact that I am a sinner and yet I have every reason to pursue the life of holiness because no matter how miserably I fail each day, I can try again afresh. I don't need to be fatalistic about myself. You might think why I should try at all if Jesus has paid the debt then. That's because my "taste" has changed at a profound level when Jesus met me. I find it much more joyful to keep on trying and find God's grace where I fail, than to just accept my sins and reveling in them.