“You are your own worst critic.”
This is assumed to mean that you are harder on yourself and on what you produce than anyone else. This is probably true. You know more than anyone else. You see mistakes or hear a missed note. You know your vision for what you’ve created and this vision is your measure of success.
You probably do have some degree of understanding if something is working or not, but that is where it ends. You are entirely too familiar with and invested in your work to know how good or bad it is. Your understanding is subject to all sorts of tampering. You’ll find your own criticism of your work is usually more about meeting some ideal you’ve imagined than a fair evaluation of the work you’ve actually done.

While I can still stand behind this definition and agree that it has some value, I think there is a more helpful meaning. There is one that can do more to guide us and provide a bit more nuance, one that puts our focus where it should be.
I think the phrase means that you are in no position to evaluate your own work. Criticism of your own work is not good criticism. It is flawed. Your criticism is not balanced. It can’t be. It is not objective.

It is surprising how often my peers walk into the graduate writing workshop and make small talk before class starts about the work we’re about to workshop – their work. They say it is awful, just not good at all. Sometimes this depreciation of their work devolves into apologies and discussion of the next draft, as if this draft – the one we’re about to look at – is a loss.
This is not only bad form, but it is also making a terrible assumption. While it assumes that you can objectively evaluate your own work, it also assumes that the discussion we’re about to have in workshop is academic, that the outcome is set.
I’ve gone into a workshop submission very unsure of the quality of my writing and found my readers appreciated it more than I did. I’ve also gone into workshop with a piece that I thought was working quite well, only to received feedback that it wasn’t – feedback I could objectively only agree with.

You are your own worst critic, so find someone else to review your work. Put your energy into finding your own best critic, and then trust them to do their job. Make them your reader.
Your job is producing work. Focus there.