Inner critics are fun to deal with. You know how? You turn them into allies!!
First off, realize that your inner critic has some positive intent in criticizing you. It's not just yanking your chain because it doesn't have anything better to do, it is trying to do something positive - you just might not like the _method_ that your critic is using to get the outcome.
Armed with that knowledge, it is much easier to approach your critic. Talk to it. Tell your critic you realize it is trying to do something good for you, thank it for it's concern and attention, then ask your critic what is it's positive intent in criticizing you. I think you'll be surprised at the answer and probably agree that it's goal is worthwhile.
Assuming that you agree with the critic's intent (if you don't, that is a whole other ball of wax), you can then start negotiating with it. Explain how the criticism makes you feel and ask something like, "If we could find a different way for you to achieve your positive intent, would you be willing to try it for a while to see if it works as well or better than what you are doing now?" Your critic will probably agree, because you are giving it the chance to accomplish it's purpose better than it is doing now.
After you have agreement, start brainstorming. How could your critic talk to you in a way that would be easier for you to listen to? Softer voice? Gentler tone? Maybe if it spoke from a different place? How about positive statements instead of negative?
As I said, turn your critic into your ally. Make it your partner in achieving the goal. It may take a little bit before your critic will talk to you. You have probably spent quite a bit of time telling that voice to shut up and that you don't like it, so it might be a little reluctant at first.
Good luck and have fun with it .