A good start.
Sometimes, having a specific aim when you write a piece of music can be a very good thing; it gives you direction, it gives you a sense or idea of where you are going and how you are getting there, among many other things. The only thing to ever watch out for is that your imagined world doesn't get in the way of your musical vision, so to speak.
Now on to the review...
The strings/piano combination is a very popular one when a newish/amateur (not in the bad sense) starts off writing music that he/she deems 'classical'. This is because both of the sections in question are very expressive, and useful for communicating easily any overlaying message the composer has. The flipside is that this has a chance of limiting the overall expressiveness of the piece by limiting it to a few instruments. Sometimes, in a string quartet, this is not a problem, but for larger-themed pieces it can be. That said, I think in this song it veers a little close to that area. Not completely, though. I would recommend, if you should try this style again, experimenting with using more instruments to say more things, to make more ideas made tangible for this listener.
Also, key to composition is utilizing your instruments to their fullest, and bere is where I think some good constructive advice is necessary. The strings and piano here mainly never leave a general area of the scale, and I feel that this limits the piece from being everything that it can be. They all hover around the same chord progression, never going much higher or lower than that. You wanted to capture sad nostalgia, I would explore that idea completely! Having the piano travel the excesses of the keyboard, high and low notes sounding in unison, all of these and more have a powerful effect on the listener, and it really allows you as the song-writer to breathe a sigh of relief as you explore the feelings you feel when you think up a melody. If you are confined to a single area, and the feeling conveyed is not a bit claustrophobic, then in my personal opinion, something is lacking.
This is not to disparage the melody or makeup of the composition, though. This is to push you, should you continue to write music like this (or any music, for that matter) to not confine yourself to a small set of tones and trying to make a melody out of that. A good composition fully explores things, it leaves no stone unturned. It doesn't matter how many instruments are there; what is there is enough for the song to communicate, or to even reverberate some thing about life. If a song can do this, then it really is worthwhile.
All in all, this is not a bad song by any means. It merely lacks an imprint that can make someone say that"This is a ViceOfFire work". I think if you can find that voice, it will be so much the better when you write songs like this. Hope you continue on.