I used to feel somewhat similar in the past. I had a core group of good friends in Jr. High that made my life unfathomably better. As I got into Uni, we started to drift apart and I panicked. I struggled and resisted letting such an important part of my life and identity dissipate but it only seemed to stress things further.
The more I tried to salvage (particularly with my best friend) the more I felt frustrated with how different everyone had become in the blink of an eye and so I reacted with fear and anger which made things worse to the point where I was the one ending the friendships. Eventually I was left with only my best friend of 10+ years, and despite us both becoming very different people and fairly incompatible we kept holding on to old history and a feeling of obligation while hating each other's guts but scared to death of losing each other.
My attempts to make new friends always seemed to fail as I just never felt a spark of companionship or values that would lead to anything. Even people that were pleasant enough to be around, and has similar interests would quickly annoy me and I would start to dread spending time with them (doesn't help that I am introverted).
Long story short, I eventually decided to break off the lingering terminal patient that was my closest friendship and move on to discover myself, alone. What I found was solitude, but not loneliness as I expected. In fact I felt much more lonely back when I was nursing tenuous relationships that were on their last leg.
Nowadays I come off as more interesting and confident to people I meet and potential friendships spring out of nowhere, even though I don't spend a ton of time with new people. Being a INFP (if you buy into that stuff) I still haven't found the same depth of friendship I had before, but I am very content with myself and able to handle the interlude of solitude until I find like-minded people to hit it off with.
My advice: Don't fret about it friendships, you sound like me with your romantic view of platonic relationships which may be hindering you, since most people become friends somewhat by circumstance and convenience and don't put as much thought into it. Be alright with yourself first and just let things happen organically.