That's a beautiful song. Thanks for sharing it.
Not having ever heard the song before, take what I'm going to say with a grain of salt. I have the feeling throughout the song that you're trying to sing it the way it was sung in the original version (see prior sentence, I could be wrong). I just felt like the vocals were tentative, kind of holding back. As you said, you had just learned this, so that may be what I'm hearing. I think your voice fits this song pretty well. It seemed at the end that the range might have been a little high for you. If this is the case drop the song down into Eb, D, or Db. You may find you're in a more comfortable key to sing and play.
Jef