Yes, you made a mistake and you acknowledge that and are sorry that you made that mistake, now don't beat yourself up over it any more, it's too self destructive and in this case unnecessary, it's not you who owes his girlfriend anything (unless she was a mutual friend or something). Everyone has made a mistake they have to live with and this is not the biggest one you could ever make or even close to it, in the grand scheme of things, you are not the guiltiest party in all of this, it is your friend who is the cheat.
Now, with regards to where you can go from here, you have four options.
1) You can forget it ever happened. Ignore your feelings for him and carry on as normal, as the good friends (though I'm inclined to agree not 'best' friends) you've always been.
2) If you can't carry on as normal then you can avoid him. If your feelings are too deep to bear seeing him without being with him you will just have to cut off contact.
3) You can tell the boy how you feel, which could risk your friendship but it also could push him to break up with his girlfriend and be with you. I'd make very sure that your feelings are real and not just confused as a result of the sex before you take this action though.
4) You can try and seduce him whenever you fancy and not give a toss about his girlfriend, although, if you do have genuine feelings for him you could end up getting hurt and feeling used if you accept this option.
For what it's worth, when I was in this situation I opted for number 1, I thought I loved him for years to be honest but now I'm very embarassed that I ever had any feelings for him like that at all! (and our friendship has lasted longer than his and his girlfriends relationship and certainly longer than a relationship between ourselves would have lasted had we gone for it. In a years time this will not seem like a big deal I assure you.)