I've tried the game again and I was able to eat all the meat with your suggestion. I think that all the action that happens in the moment where you grab the meat and start to run makes it easy to miss the arrow. Perhaps you could introduce that mechanic before some way so that the player already knows that he should pay attention to the arrow.
On a sidenote: somehow I managed to jump over the wall on the right and fall out of the level (that made quite easy to eat the meat :D).