Customer complaints are a fact of business. A customer who takes the time to complain rather than to take their business elsewhere may well be speaking on behalf of the silent majority. If the complaint warrants a systemic change or if you have taken action as a result of the complaint thank the customer for bringing the matter to your attention and advise them on the corrective steps that you have taken.
Implementing a system to deal effectively with customer complaints and to turn them into raving fans is a strategy that we have used to good effect in our business coaching assignments, so go on, give it a try!