I'm concerned about a red light which stays on when the car is powered off.

Hello, your red light is merely an anti-theft deterrent if it's the one that blinks occasionally. All other lights will go out after a short period of time. If it is in the anti-theft light, it will not drain your battery at all. If some other light is on bright and solid, I would recommend seeing your local Honda dealer, as your CR-V is likely still under warranty, to have a look at it. My guess is that it's normal, and I appreciate that you're being cautious.