Sounds like the gearbox bearings; you could check the oil level though. When you accelerate you are putting force through the gearbox but not when you take your foot off. If it is quiet when coasting in neutral but noisy in gear and putting power on then it must be the gearbox; nothing else it could be really except amybe CV joints but they tend to click on turning or growl badly.
What mileage has it got?
When idling does it make a slight noise which goes if you press the clutch down? Civic gearbox input shaft bearings are a 'known' problem.