Plumbing question: When Teflon tape doesn't stop (tiny) drips

I just installed an English bar in my basement and was hooking up a water line this evening. Before connecting two CPVC water pipes, I wrapped the threads with 2-3 wraps of Teflon tape, making sure I wrapped it in the right direction. I then tightened the connection quite well.

After connecting, the pipe dripped–just a tad–so I started from scratch, using new tape. Doesn’t matter. The pipe still drips, though just barely.

Should I be using the pink, heavy-duty Teflon tape instead of the white? Would a liquid sealant give better results?

Should I be using Teflon tape at all? Someone told me that no Teflon tape is needed if connecting two plastic plumbing parts.