How do you get oranges out of your teeth?

I eat a fresh orange every day as part of my breakfast as its supposed to be 'good for you' with the vitamins etc. However a major problem I find is the remnants of it sticking between my teeth. I do clean my teeth afterwards with a new toothbrush and also use mouthwash, but notice that brushing just doesnt get it all out, because even hours later I can still pull little bits out with my fingernail. This cant be good for tooth decay, and also the acid from the orange will affect tooth enamel too. So does anyone know a better way to get rid of this problem? Ive even considered giving up fresh oranges as other foods (apart from coconut) dont seem to be anywhere near as bad for this.