I get that a lot. My usual response is that I can play extrovert really well, but it's draining. With one person, or two, I'm just fine. With people I'm familiar with and comfortable with, like my knit group, I'm OK. With a big group, or a lot of people I don't know well, interaction is work, and there is a cost I'll have to pay in terms of tiredness, irritability, and generally wanting to hide in a cave.
Before a party, all-day company meeting, or gathering of strangers, I have a routine. First you put on the battle armour, clothes and shoes picked with a goal in mind, whether it be comfort or looking good. Next is the war-paint, tactical amounts of make-up to hide behind. You can't see me, you see only my eyeliner and lipstick. Finally there's the smile, faked or otherwise. Afterwards there will be the "leave me alone" energy crash, time when I need to recharge and be in a silent house with just husband and cats. We've been married nineteen years and long ago he moved from "people that require work to be with", to "people I like to be with even when I'm all people'd out".
Some people sit in their heads and think about what they want to say, then say it. Other people talk to figure out what they want to say, and then they say it. I've come across a lot of introverts that think first then talk, and a lot of extroverts that talk first, then say the useful thing. As an introvert, there's a lot going on in my head at any one time. Right now I'm noodling on what the plot will be for my NaNoWriMo novel this year, planning a gift swap parcel for an online knitting group, thinking about career feedback I've been getting, and a lot more. I like to consider what to say before I say it, and if that means waiting through an awkward silence, I'm fine with that. Most people baulk at silences, and around the seven second mark will jump in and say anything that comes to mind, just to make it stop. Silence is my natural environment. I'm comfortable there.
I don't see being an introvert as a disability, or an illness, or a defect. It is how I am wired. I am rarely bored because there is a lot going on in my head. I've always created story worlds when I write, and though only a fraction of that shows up in the finished story, it is the underpinning of the whole thing. But people, especially strangers in groups, require effort.
(Today I met an introvert who talks to figure out what to say, they do exist!)