Criticism is hard to take. Everyone will tell you it's something you have to accept, and welcome when you write stories, when in reality it's not. Time and time again, books that are by most standards considered horribly written in every aspect, make it to the big shelves and propel the writer to the top of the charts. Stories that are considered well-written don't make it often as people think they do.
We tend to assume for some odd reason that if you didn't make it, you weren't good enough. That's BS. There's been a couple authors who try to replicate their insane success by writing under a pen name, only to find that, despite having written the same quality work--and in some cases, even better quality work--they fade into obscurity even though they're published. Until someone discovers their pen name is connected to that one big writer. Long story short, quality doesn't matter much as people think it does with writing, and therefore criticism loses some of its assumed necessity.
So, accepting and absorbing criticism is not a be-all-end-all for writers. Still, if you want to share on the web, where a lot of people are far more cruel than they need to be, it's important to work up a resistance. Writing is very personal to me in most cases; when I share my stories, you're getting sneak peaks of some aspect of how my mind actually works, and how my characters reflect pieces of me and fight against each other. I don't adhere to many writing conventions; some of them, I take as a guide, but by no means are they rules. Storytelling to me is a creative experience that refuses to obey rules.
For a number of my stories, I write for me and only me. For other stories, I write for both me, and a hypothetical audience I hope to one day have, because I believe storytelling is one of the most powerful devices we can use to reach others. It's my way of connecting to the world, and to people, and communicating, as someone who's very quiet in real life. Given how much work I put into my stories, if I were to encounter brutal feedback that people so often love to give for their own amusement, I know I'd take it hard, so I make little steps for myself.
To do this, I'd make a short story, or some longer-term project of mine that I don't really care about. Maybe it's a comedy, or it's satire. One story I was working on was about a girl who makes badly-written romance on the Internet, with a huge following. She offends one of her superfans by killing off a favorite of theirs, and then is cursed to live in her own fictional world, where she figures out the super attractive dudes she writes about are the worst people she's ever met! Ridiculous premise, but it was fun, while not meaning anything to me, so I knew I could take any feedback on it. No one actually gave me feedback on it because that's hard to find on the Internet but...the step I took still stands.
Another step you can take, is to find someone who you know is a gentle critic. This does not mean a critic who sugarcoats. This is a critic who is completely honest, but phrases their criticism with language that's easier to digest. These people can be hard to find, as it takes a bit longer to write a nicer take on criticism than not. It takes more words, and you have to think about how you're phrasing it. A sub-step to this option is to ask them to pick out only 1 thing they would change, as opposed to maybe the 3 or 8 things they found.
Take criticism at your own pace to slowly open yourself up. You don't have to put your work out there for the entire web to see. Find some people who know how to provide gentle criticism, let them know what you want from them, and preferably find some way to return the favor. 
