I used to be really defensive with criticism because I associated it with value judgment (both my parents are really judgmental). When I finally learned to separate the two, life got a lot easier and now I take criticism well. The above posters are right, you just have to separate the personal from the impersonal. I'm still a little sensitive at work, because I know my performance matters there; what people think of me and what I do has an impact on my future and job security. But I've learned that at work it is totally impersonal, and to just look at whether what they are saying is true. I know being an artist isn't the same as working in a restaurant. But remember, critique is always what someone else thinks. It will always be subjective. The nature of art is to appeal to people's preferences. How well you meet certain goals (such as realism or good composition) with it is kind of objective, but once again it is someone perceiving that. Their subjective perception might enable them to see something objective about a piece that you miss, and depending on whether a lot of people perceive the same thing your art might be considered "better" or "worse" (along with people's personal preferences). But in the end you have to decide 1) how well does this meet my goals and how much do I like it, and 2) does it have the desired effect on people. Also remember that often people find negative things to say because they're jealous.
I am an artist too. I don't do much visual art anymore, but when I did I actually don't remember many critiques. I was used to getting compliments and positive feedback. When someone would say something less than positive I tended to think either they must have a point or they were biased in some way, and that's what I think now. My version of perfectionism is my art not accurately reflecting what I see in my head; which is good for not being sensitive, because I can look at the art as an object. It doesn't really have to do with me. What is in my head and my unique talent is mine, but that's not what they are seeing. They are seeing my attempt to put that into reality. And if I didn't succeed, oh well, I can do it differently next time. I always just evaluate what they are saying and decide whether i think it is true. If not that's just their opinion. If so, it is helpful.
FWIW I like your art. I don't know what the particular goals for it are, so I can't say whether it meets them. Obviously it isn't meant to be entirely realistic, so I don't see the point in looking too much at that. The only point there is that in the first one the leaves of the tree kind of look the same as the background and it is not obvious they are part of the tree. But this is really not important to the overall effect of the picture, so I wouldn't obsess over it. I actually think the anatomy is good, for being animation style. Nothing stands out at me as being off. Your style is cool. I like the bunnies. And I like the way things are not exactly what the viewer expects.