We all have varying opinions of alcohol, but for a lot of people, alcohol is a way to loosen up and be comfortable at events. As this video by Charisma on Command explains, you can do that and talk to people comfortably without it, even if everyone else is buzzin'.
The idea of "faking it 'til you make it" captures the spirit of the video's tips because it's really about changing your mindset and then taking action. First, they suggest you think of this is as a personal challenge. Plan and intend to be that talkative and energetic person you think you become after some alcohol, but without alcohol. This way that intention carries over into your interactions.
The second tip complements the previous, where they suggest essentially the fun version of power posing. And finally, they just come out and say it, "Stop going to events that suck" (of course, level of suckiness can vary.)
But rather than simply telling the person who invited you no, try throwing out a counteroffer, where you politely decline and swap it with another idea for a get-together (sans alcohol most likely). This way something fun is still on the table and you don't totally shun the person for inviting you. Check the video for full details.
How to Have Fun Without Drinking [Charisma on Command]