How can I stop a small leak at the back of my high-cistern toilet?

I've just moved into a house with a high-cistern toilet & have noticed some discolouration at the back. When I checked, the metal pipe that connects the cistern to the toilet appears damp around the connection to the toilet bowl, and seeps slightly (not enough to leak properly). I've tried turning the water off to the tank & flushing the remaining water through, but there must be some water left in the pipe, as it doesn't seem to dry up. I tried silicon sealant, but the small amount of moisture stopped it setting. Is there anything I can use, while it's still damp/wet? Any other ideas? I'm new to DIY, so unless it's a simple fix, I'll probably end up with a plumber...