Beethoven's Fur Elise?

Okay, well I just started piano lessons a couple weeks ago...but I had started playing last August and taught myself Fur Elise(with the music for it of course!) Anyways I kinda cheated, because at that part where your left hand goes up and plays(how do I explain this) the two C's and then E and then your right hand plays that same E and your hands just go up playing E's(if it helps, this is repeated 4 times throughout the whole song) I just play the two C's with my left hand and then my right hand plays the nest two E's then my left hand plays the next two, and then it kinda goes back and forth if you know what I mean. Anyways my question is, is it really a big deal to have the original for this because my teacher seems to think it is...and was this song difficult for you to learn? When I was learning this song I found that I got wicked messy at that fast up and down part, but I've gotten better. If you have any other thoughts please tell me, thanks. ^.^