Well, I should qualify that. Do apologize if you step on someone's foot or are an inadvertent jerk, but don't apologize if you're trying to create a masterpiece of some kind, and it falls short in your eyes.
There has been a lot of apologizing in my fiction writing course lately, and I say people, STOP apologizing for your work.
My partner and I always joke that it's too late to apologize.
Seriously, though. You are where you are, and that's just part of the process.
Ira Glass said it so well here.
As my acting teacher used to say:
You aren't the best; you aren't the worst.
So, let's put our egos aside and focus on the work.
Instead of saying, "I'm sorry," say:
Because at least you're trying, and that's more than many others can say.