How can I obtain a refund for canceled Apple Music subscription?

I forgot to cancel my automatic payment for a subscription in one of my online payment apps. I had given permission for it to automatically process payments. However, yesterday I canceled the subscription through Apple’s settings, but today the subscription fee was still debited from my account. I did not receive the subscription nor a refund, even though I canceled it. I have now disabled the automatic payment system. How can I obtain a refund?

[Re-Titled by Moderator]