I'll take a bit of a different approach and talk more about how to handle it emotionally:
- It's okay and normal to have thin skin!
Don't listen to people who call others 'babies' or 'snowflakes' with a 'fragile ego' who just need to 'toughen up' and need to be 'knocked down a peg' with a 'reality check'. Or that 'good artists learn from criticism and don't feel attacked by it'.
It's absolutely unnecessary and counterproductive to shame people for having feelings. If you feel hurt by feedback that says your work is less than stellar, you did nothing wrong, and it says nothing about your talent or worth as a creator! The only thing that matters is how you act in response; for instance, if you ask for feedback and then lash out at someone who accidentally phrased theirs a bit rudely due to lack of social skills on their part, then yeah, that's a bit douchey of you, but if you just want to yell at them and call them an asshole but don't actually it, you have every right to feel that way :] Which I guess leads onto my next point:
- Don't give substantial responses to your critics until you've calmed down a bit
And if you didn't ask for the feedback, you're not obligated to respond to them at all, ever :] But if you want to discuss the feedback and points you may disagree with them on, doing so when you're still emotionally reeling from the critique is likely to make you look defensive, and people who like watching creators squirm are going to latch onto that. Only give thorough responses if you've carefully considered the criticisms and have firm points of rebuttal, otherwise a simple "Duly noted, thanks for your time!" will do 
- You don't need to consider the criticism and put it into action immediately!
It's unfair imo to expect creators to look at a critique and immediately go 'oh, you're absolutely right, I did do X Y and Z wrong, you have opened my eyes!' If the criticism was especially harsh, it only makes sense to look at it once you've recovered from the sting of the delivery, and be more objective about what they're actually saying.
But even aside from that, it takes time to absorb criticism. It's similar to how you can't just read a tutorial and immediately be able to put it into practice perfectly; you can't just listen to someone telling you that you did X, Y and Z wrong, and immediately understand why, or do it right this time even if you agree. I've had criticism I've received years ago that made me go 'wtf this guy doesn't know what they're talking about', but now see the sense in. Just because I dismissed it then doesn't mean I didn't learn from it!
Take your time. The critique isn't going anywhere.