Define a complaint. ISO 10002 calls it: 'An expression of dissatisfaction made to an organisation ... where a response or resolution is explicitly or implicitly expected.' It's a complaint whether it's delivered in writing, by phone, e-mail or any other channel.
Encourage complaints rather than suppress them. As the old adage goes: 'If we're doing something right, tell your friends; if we're doing something wrong, tell us.'
Record it. The reasons for logging complaints are several: you can analyse the cause to identify trends that indicate bigger problems; monitoring the number of complaints gives a measure of your customer service; and a tracking system should ensure that every complaint is resolved or responded to.