Role of QA is not to find all the bugs. QA is there to establish a process of finding bugs, collecting and prioritizing them, to be fixed fixed by developers in order of business priorities. And provide business side with info about current and projected stability of the codebase, and if release is stable enough to be released withing the deadlines.
Quality cannot be "assured" by more testing - quality has to be designed and coded in. In famous saying, QA cannot prove there are no bugs - can only show where known bugs are, using the limited time and resources QA has to do the testing.
Quality is a team effort. Developers, QA and business side all have integral part in assuring the quality, and finger-pointing is the fastest way to hell.
So if customer found a minor bug, and QA was blamed for it, business side failed to do their job. Proper response would be emailing the customer:
Thank you for notifying us about the problem. Your comments were entered to bug database and they will be evaluated and prioritized by severity and how many customers they affect.
While I cannot tell you right now when your complaint will be fixed, I can promise it will be taken seriously.
I would also like to thank you for our using our product and for taking time to enter the feedback. Feedback from customers like you helps us to improve our product and make it work as best as we can for as many customers as we can.
If you have more concerns, please do not hesitate to contact me again.
This is the role of business in the situation like yours (with a minor bug). Cover your back, report the bug, not throw you under the bus.