Hi there.
Just to mention beforehand, I have some experience in this area, learned electronic piano till I was around 13 years old, then played the Alto saxophone for 6 years. I do play some Tenor, but Alto is my favourite. During that duration, I'm also in the concert band of my school and was the president of the band for my last year studying in the school. So I do have so-so knowledge in tunes and music theories.
Anyway, lets cut to the chase. I took some time to hear your song out, and it is indeed above average, but do try to practice some of the pitch there.
This song sounds like it have quite an amount of sharps and flat tones in the singing, although I've never heard the original version though. However I must stress that everyone have their own range of tune when it comes to singing and some may not sing what others can, or vice versa. So it's even better to know what your range are and sing songs that suit you, or you can change the pitch of the song itself.
What I can suggest is try out this free
Voxal Voice Changer. I do perform some recordings and music creations and I find using it helps to ease the later editings. First you can try out the Concert Hall to alter your voice recorded. Under it, go to Reverb and change Decay to somewhere around 500ms ~ 1000ms and probably the Diffusion to the value 10, lastly the gain to around 80% to try and cancel out the wind/fan/noise in your recording (if any). This is what I use for most of my recordings.
I also save it as Singing so I can just use it whenever I'm recording. Play around with it since the optimum result may vary for different people.
Another free tool you can explore is
Audacity. Here you can then probably tweak your recording, remove noises, enhance the bass of the music, or even change your pitch slightly to fit the song even more. But usually too steep pitch changing will have weird result though.
One more thing is probably you can increase the volume of your recording in contrast of the background music. Either sing louder, or edit it later on.
since in your sample mp3, your voice is somewhat covered by the music and this shouldn't be the case for songs like this. These songs stress the vocal power. I think with the help of the setting with Voxal that I told you, you should be able to achieve that.
And remember breathing is the key. Having sufficient breath can really make the difference when it comes to the quality of your voice/tune when singing. Having suitable breathing exercise benefits alot for singing. Try to breath into your tummy. Ever seen babies while they're breathing? their stomach expand when they inhale instead of their lungs. If you have a hard time doing it, try lean down on a flat surface or your bed then put a slightly heavy book/object on your stomach. The weight isn't necessary to be very heavy, just enough for you to feel it go up and down when you breath into your stomach.
Lastly, perhaps you can do this cover again with the help of the tips/tools I gave you?
would love to see the result. I apologize for typing such lengthy comment though. I tend to type alot when it comes to explaining or I'm just too indulged into typing all I can think of.
EDIT:
I've listened to the original song. This song is amazing indeed.
Can't believe I've never heard it before.
Another note I would like to give is about the vibrato. This song does sounds there's lots of vibrato, which is vibrating ending when he finish a sentence. example, Forevermo-o-o-o-orr-oree~ Vibrato adds more feel to the song and I'm sure it's common in this type of music and oldies. Vibrato actually came to me after I've played the Alto Sax for some time, since Vibrato in saxophones are very common. Since then, I've been able to add some vibrato to my singing, but still have lots of room to improve. Perhaps you can try to duplicate the effect of vibrato while singing songs by literally singing like it. After some time, you'll get used to feel and it'll come naturally without hard attempts.
Or just look it up in the internet. The internet is just full of tutorials about anything nowadays.