Creativity site 99U suggests one way to better handle negative feedback is to start asking questions that will lead to a real solution.
Getting feedback is tough, and it's incredibly easy to fall into a defensive or aggressive trap when someone doesn't like what you're doing. If you really want to make the most out of the experience, you need to find a solution to make it better. One way of doing that is to ask the right kind of questions:
To ask a solution-focused question, describe a potential solution and ask whether it would be acceptable to the other person. For example, to get a piece of work accepted in its current form, you might ask:
"I know you don't like the look of it, but if I can show you evidence that your customers prefer it this way, will you sign it off?"
Your goal is to leave the room with a clearly-agreed next step towards a solution. They may still be sceptical or unsure, but at least you know what you need to do to get the work accepted.