Exactly. I'm quite introverted, and I have no problem reaching out to people to cancel plans. It's easy, just send a message like, "Hey, I've got a conflict, can we reschedule?" That's it, and 95% of the time they respond with something like, "Sure, the time wasn't good for me either" and it gets rescheduled at some point, or not at all.

Introversion has little to do with social anxiety. Introversion is about comfort and energy. When I go to a party or other large social event, I come home drained and often spend an hour or two reading or playing video games (single player; MP feels social) just to wind down. I may have enjoyed myself, but interacting with other people takes effort. My cousin is an extrovert, so after a big social event, she wants to go to an after party.

You can be extroverted and have social anxiety, and you can be introverted and have no social anxiety. They're orthogonal concepts.