I think it´s a perfectionist problem to try to make the social interactions as flawless as possible. But - some "flaws" here and there can actually make the communication, paradoxically, deeper and, if that´s your thing, better. It´s hard at first, but you could just try to force yourself to spend more 1) "superficial" time with people, and 2) in longer periods of time.
1) Why superficiality isn´t really that bad? Because it´s not just what we concretely do that matters, but the "underlying messages" that we share with each other via spending time together. We don´t have be perfect all the time and say all the right things. Come on, we all know we´re not the perfect people we often would like to appear as. Being with people is sharing a human experience with them, not a performance stage where we should perform perfectly. If you like some person, they like you back, and you two want to spend time together, nothing else matters. Let yourself be vulnerable, and trust that you´ll be accepted.
2) When you´re with people, there will come those moments when you think to yourself "OK, I no longer have mental energy left, I want to go home". Fight it. Again: let yourself be vulnerable, it´s okay that you´re not all the time "functional". It just makes you more human and deepens the relationship (!). Hey, you have very humanly feelings as well, who could have excepted?
I´m working with these two points myself as well. Especially not escaping the social situation was/is hard for me. But really, just believe that people will accept you as you are, no matter if you said something stupid or you were tired. It´s understandable. We all think "stupid" things sometimes; not saying them out loud doesn´t mean they aren´t there. It´s actually pretty freeing when you can say them out loud and see that nothing bad happens. Your IQ doesn´t suddenly drop, it´s still the same. It´s just a closed-minded stereotype that "intelligent people are like x or y, but never z". Nah-ah nuh-oh.
Letting yourself to do something that you might, right now, perceive as "flaws" or "mistakes" can actually be the spice in the soup. The relationship will mold itself during time. One funny thing here and there, they just give the relationship more depth.