Atually, it works the other way around too. If you go ahead and use your compound or rifle, you may very well finding yourself thinking afterwards - "I could have done that with my longbow!"
Personally, I've gotten over that feeling completely. I might regret a mistake I made in set up, poor shot, or whatever caused me not to take the animal, but I don't regret the weapon in my hand at all. What I hope will be my biggest screw up of my life was when I shot over the back of a 320 class bull elk at 25 yards. I think about that miss often, but I honestly don't think I have ever regreted carrying a recurve that day.
If you really do have the need to kill something then maybe the longbow is not the best weapon for you to carry. And there is really no shame in that. It's all just a matter of your own personal priorities. Do what is right for you, and don't worry about what anyone else thinks.