Outside the formal anxiety sense, most people struggle with the negative feedback loop. The trick is that you can't simply turn it off - even if you're the best socializer in the history of humanity. For me, I set an informal timer (usually while journaling or in the shower) to intentionally introspect my interactions and pick one thing I felt I could have improved on ("I really wish I had said more than 'fine' when So-and-so asked me how my day was") and then move on.
One lesson that's hard, for me and I suspect others, is that while it's very important to be polite, it's not your job to make everyone else feel happy or complete - that's not an excuse to go around being a jerk, but also don't feel you owe anyone else something by default. It's enough to have a conversation about the weather or let the other person complain about their boss some and offer a bit of empathy.