When customers complain, it is obvious that they care enough to make that call or email that grouse. You could argue they only care about themselves. And that is precisely why you should care and use that as an opportunity to out-care them than your competitors.
Make your apology real. Say, “We are sorry.” Make the compensation worth it. Be generous with it. I know, the common fear is, “what if every customer did the same and take advantage of us?
The answer is this, when customers make complains they first want to be heard. They could be angry, frustrated, disappointed. They want a listening ear and they want you to fix their problems with your service or products. Maybe 0.05% of your customers have fleecing you in mind. But by and large, they just want to be heard and cared for.
If you can up the caring, you may have just recruited a brand evangelist.
Who is going to care on your behalf?