Michelle has some great ideas there.
I have to say that I struggle in certain social situations. For this reason, we tend to prefer smaller functions. I can chat a lot more easily at, say, at dinner party for six than at an event with many people who I don't know. Hubby also used to introduce me to people who can talk easily and who I'd get along with and that helped heaps - but now I know all his friends and am fine on my own. I've also gotten far better at small talk with practice.
The thing Michelle said about compromise is the most important though. We compromise and it works well. But my ex-h was so introverted that he'd virtually make himself ill with nerves before going out. I'd go as far as suggesting that he developed some type of social phobia. My ex wouldn't address the issues (which is one of the reasons he's an ex), but if your guy is as bad as mine was, I'd suggest that counselling be an expectation if this relationship is to continue.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.