Art criticism can be negative or positive. Both of these things can still end up as a positive if they are constructive and not opinion based. Negativebut constructive feedback is when someone says - "I think this painting could use more contrast." and you suddenly see how that could be acheived and how much of an improvement it would make. But sometimes the statement being made is just plain mean! Here's how I like to deal with negative feedback.

First and most important - categorize the negative feedback and the intention behind it: 

Ignorant - The person doesn't actually know how to speak about art and their feedback doesn't actually make much sense and seems really out of left-field. Dismiss this feedback and if you want to be polite this one word answer can be sooooooooo helpful, "That's interesting".  

Opinion - "I don't like this" or any more polite or more rude iteration of this. "My art doesn't appeal to everyone" or "My art isn't for everyone." If some one is particularly mean-spirited about this then you can respond with inspiration from "the dude" in the movie The Big Lebowski and use the come-back in the video clip below: 

Constructive - the spirit of this can be well-intended or mean-spirited. The response if it's mean spirited, "That's one way to approach making art, but not the way that I chose/am interested in." or "That's not the look/idea that I'm going for." . If the feedback it constructive and mind-blowingly wonderful then a simple "thank-you!" will suffice. You can take the advice or dismiss it - the choice and the power are yours.

Video source [1]