I think you have a good start
There is an idea here (more on that later), and some good imagery - I like the "frozen blue eyes melting" image for example.
Let's see if I understood the story right.
It seems that someone feels guilty about an old relationship. They don't want to restart it, but do feel bad about their behaviour. The girl started happy in the relationship, but became disillusioned, and the boy felt that he led the girl on and that it is his fault?
Is that about right?
It's a tricky story to tell.
I'm with Ido in that this doesn't feel like an apology. If it is one, it isn't quite clear what it is apologising for. But there is a story there.
Hmm. You could tell this in a number of ways. You have chosen to do it by addressing her.
That can work, but is challenging. You have to be careful that you aren't talking down to her, and be accurate about her feelings. When you sing using "you", the listener will hear it as if you are talking to them. This can work if you are apologising, but not if you are just explaining what happened. You need to make the listener feel good and it would be easy for them to challenge your version of events (I know, they weren't there, but the object of the song is now a symbol they can relate to).
You need to make "her" understand that this is about your need, not hers. She is the one doing the giving.
You could make this something that happened a long time ago. Maybe you are now middle-aged and you are talking about a first love? Time removes the sting.
You could tell me about this girl you used to know (in which case it needs to be in the 3rd person). That may be easier, but could also be less effective. You need to find a way to make it interesting to me. It would become a confession rather than an apology.
You could write it from her perspective even
OK.. the lyrics themselves...
"I met you a long time ago, and I haven't seen you since"
.. nice.. could be strengthened.. "I loved you a long time ago .."?
"I messed up our relationship and wanna make recompense"
Do you want to "make recompense"? "Make recompense" sounds a bit formal and legalish to me... one to play with.
"Not because I feel I love you or want to make it work"
What does "I feel I" add here? Did you ever love her?
Make it work? I know you mean you aren't trying to start over. It just sounds as if there is a current "it" to make work....
"
Just because you deserved better that alone makes enough sense
I can clearly remember that smile that crept up on your face
A pleasant look of contentment a look of blasé replaced"
May be hard to sing, but I can't tell. The intent is good here.
One small thing .. you can't have a look "of" blase. A look can "be" blase. It can be a blase look.
"
Your blue eyes that were frozen soon were melting down your cheek"
I like this line very much!
"
And I held you for forever while the world around us raced
But theres no more sense of desire, and that I cannot change
Its just the way my heart beats, to try would just feel strange"
All good.
"
So I apologize for leading you into uncertainty
And for even meeting you at all because I know it caused you pain"
Hmm. I think you can rework this bit. I don't buy it. Do you?
Overall, I think you have a good start here, and thanks for sharing it! I don't know how you work, but I find every song starts for me with some lines that I am pretty sure are "keepers" and others that I can't quite feel satisfied with.
This feels like a song at that stage, and feels like it could be a little gem that just requires some polishing. You never know until you get to work!
Get some mental pictures to go with the song, add some little details to make it feel real - then work on the lines you feel are weakest. Make it fit your picture. Is it something you would say? How would she react? Does anything feel out of place? Could you add anything that shows that you (really) understand her perspective?
Write more, and cut the bits that don't fit.
Sometimes the song changes shape as you do this, and that can be good too.
I'd love to see it develop, and I'd love to hear it when you are ready to share.
Seriously, I wouldn't have bothered writing all this stuff if I didn't think it had something.
Good luck!