Hello there, formerly 27 year old virgin here, currently 29 year old non-virgin. I can surely identify with those feelings as I struggled with them as well. As you did I even thought about them in the concrete terms as directing anger either outwards or inwards. In my experience every impulse to direct the anger outward should be stopped, giving way to that only makes things harder for yourself as well as obviously not being fair. Other people are not responsible for ones lack of intimacy.

On the other hand directing it inwards just hurts a lot and can get almost unbearable. Can't say I really found a perfect answer to this dilemma that both sounds like the proper way of dealing with it and actually works in practice. However what I did was release my anger on myself in short bursts that didn't interfere with my social life in the way feeling this constant feeling of self-loathing at a party does. As stupid as it may sound I basically barraged myself with negative thoughts sometimes like "you are a ugly pathetic loser that's completely uninteresting to everyone".

I didn't actually buy into the thoughts but it got the tension out and after whatever time necessary I spend self-pitying and self-loathing I said "that's enough" and went back to thinking positive again. It's like calling yourself stupid to alleviate the pain of accidently hitting yourself on the thumb while hammering. But you can't buy into it, it's some kind of comfort, not truth.

Secondly I allowed myself to feel sad sometimes about missing out on intimacy and realizing I was envious of others. It is real sorrow, you can't get around it. Sometimes I cried but mostly I just felt sad. The important part is to not get stuck and remember that whatever intimacy you may have missed out on compared to others lies in the past. It is as lost to them as it is to you. What matters is the future.

And lastly, if you are not medicating for depression, then that's probably a good idea.