Err what? Could you please not put words into my mouth?
Also 2 things here:
One: The EU's influence on domestic affairs was minimal at best. Yes, they have brought economic regulations, but most of those regulations or very similar ones were already in effect anyway. And then there's the social-politic regulations which are by far more on the liberal side. The EU stands for equality, anti-discrimination, and freedom of thought and expression.
Two: The UK had plenty of influence on these regulations. They just weren't the ONLY people who got to decide them. And to top it off, the UK didn't even have to adhere to many of those regulations anyway.
Also yes: Having the personal freedom to choose where I live and what education or career I pursue is liberty.
Having my personal liberties clipped left and right and, in the worst case scenario, having to finance a failing country with my own small income while the Farages and Borises and Camerons laugh and squeeze the last few pennies out of the economy for their own enrichment, in my opinion, not a very liberating existence.