It's hard to explain to some people that on my days off, I actually plan to do nothing. I work full time in the summers, and I'm exhausted and all I want to do is sleep and play video games. I've always been the kind of person to shy away from people, but honestly, I can see that it's gotten worse as I've gone to college. Yes, sometimes I'll go to parties, but it has to be an important one. Or more likely it has to be at my own house.
As a child, I would always be reading and keep to myself. I had friends, but to go out places, they had to drag me. Same usually happens in college. But luckily, my group of friends now understand when I don't want to go somewhere. They understand that my job, since I'm surrounded by thousands of people a day, drains me of any type of extroverted means. I work at Universal Studios Orlando, and I have to talk to hundreds of people a day. As an introvert. It makes me tired by the end of the day where I don't want to talk to anyone. I'll come home and just pass out or I'll watch Netflix or I'll play a game. My boyfriend is the only person I'd want to talk to after work, and I feel like it's mostly because we have to Skype to talk each other since he lives in a different state. Since it's through a computer and we're playing games at the same time, it doesn't feel as draining as if I was to sit in the kitchen with my roommates and chat.
Your introverted friends love you, they really do. And it's not an offensive thing when you drain them of energy. You just might be extroverted and they can't deal with being surrounded by people and talking all the time. They won't enjoy themselves, so they just end up not going. I don't go out half the time because I think "why waste the money on gas to go there if I'm not going to have that much fun and just want to leave the whole time." I have gone to parties and sat on a couch by myself for like an hour on my phone, because I won't make an effort to talk to people if I have nothing important to really say. It's worst when I have to be the designated driver, because I won't abandon my friends and I know they're having fun so I can't leave. I've brought my phone charger to countless parties when I actually used to go. Actually I don't know which is worse, being the sober or not sober one. When I'm not sober at a party and someone else is driving, I'm literally stranded at the party and can't leave whenever I want.
What extroverted friends need to understand about their introverted friends is that if they don't want to go somewhere, don't force them. Especially if you're the type of extrovert that halfway through the event you ask the introvert "what's wrong" when they're sitting by themselves at the party and get mad to the response "nothing, I told you I didn't want to come" because you can't force an introvert to have fun like that. They have more fun sitting at home reading a book, playing video games, watching TV, or just plain doing nothing. And it isn't your place to judge, because in hindsight an introvert can't understand how going out all the time is fun for you.