No, you're just reasonable and you make an effort to be emotionally intelligent.
Cutting the cord with these two people means that this is going to hurt for a long, long time. If it hurts now, it's not going to stop hurting until you figure out why there isn't any reason for it to STILL hurt, and if you cut the cord with your friend and (now ex-, presumably) girlfriend, you're not going to figure that out, because there will ALWAYS be a reason for it to hurt, specifically, that it ended two relationships that presumably added goodness and joy to your life up until then.
In other words, this is going to all make sense and you're going to stop feeling hurt about it when you forgive both of them.
Now, this doesn't mean you need to tell them "it's OK that you guys did what you did, I'm OK with it, don't worry about me, blah blah blah." That's not forgiveness. Forgiveness is not saying "that shitty thing you did was actually no big deal." There is nothing that is going to make this "no big deal." It is clearly a big deal. They have clearly done a really, really shitty thing. Nothing is going to change the fact that they have fucked up, BIG time.
So what you need to do (after calming down enough to do it reasonably, and maybe letting some anger out in a safe way somewhere with a sledgehammer and some surplus computer equipment you find in a dumpster outside an office building or something) is (a) ask them what they were thinking and why they thought what they were doing was a good idea, both individually and apart (it'll be interesting to see if one of them holds themselves more responsible than the other), and then (b) adjust the story you've been telling yourself so far about your relationship so that it makes sense, because right now it doesn't, and that's what's causing you so much pain (you thought you had a good thing going, and then your trust gets flagrantly violated and a whole lot of cognitive dissonance starts happening because you thought she was into you and suddenly feel like you have to revise your opinion).
Trust me, there CAN come a point where this will make sense and you will be happy to say "you two fucked up big time, but people make mistakes, and as big as this one was, I'm deciding to make it a safe mistake for you two to make, so that you can be free enough from guilt to get down to the business of learning from it." I'm not saying you somehow need to get to this point, but it'd be optimal.
Either way you'll probably end up staying single after talking to these two. Continuing the relationship sounds like a pretty risky plan. But considering this unforgivable is just deciding to be in pain about it for as long as you can remember it.