If you can, get a 1/8" NPT to 1/8" barb adapter. Then drill a 3/8" hole, wrap some teflon tape around the adapter threads, and screw it in. The 1/8" NPT threads are just a bit larger than the 3/8" (actual size) hole, so it fits nice and snug.
I originally found the adapters at Ace, as neither Lowes or HD had 1/8" NPT, only 1/4" NPT. And, if you can wait a few days, they're also readily available via Evilbay.
You can also use compression fittings (1/4" compression to 1/8" NPT) instead of the barb, by the way. Though, if you have barbs in other places along the line, there's no real point except to make that particular tubing-to-fitting connection more secure.