There are a whole lot of different issues at play here, and I think it's more complex than you make out.
First, I agree that a referendum is a referendum – that's pretty much the end of it. Case closed. I suspect that current confusing and objection is rather a lot of people who hadn't previously been that invested have suddenly realised what the decision means, and are trying to figure out how to take the steps that should have been taken in the first place (e.g. a turnout threshold, a vote share threshold, a requirement for all four constitution counties to vote, that sort of thing.) It's too late for that, and it's a total fuck-up on behalf of everyone involved.
I think the complaints about 'social media whining' are a bit unfair. What you're seeing is a whole bunch of people who generally would support the EU, and whose social groups all generally feel the same. They are, understandably, quite annoyed at the outcome, even if they perhaps weren't as well-informed as they should be. I imagine that the majority of them didn't vote 'Remain' to 'prove a point' or anything like that, so much as they didn't have any particular objection to the EU.
On the flip side… I am sure that there are people like yourself who have a coherent, informed understanding of the EU and the associated institutions, and who have come to the conclusion that they don't agree the goals or methods of the project. Or maybe others who think that the economic benefits of escaping the single market are worth it. But I do not think that the majority of support for the 'Leave' campaign was aligned with this.
I would feel less annoyed about this outcome if what we had seen in the UK was a rational, informed debate about the future of the European project and if we wanted to be a member of that. I would have felt better if there had been a comprehensive blueprint for an independent UK – like the one that the Scottish government published prior to the independence referendum – that could be argued over. But we didn't have that, and instead got what I think Dimbleby described as 'post-truth politics'. We had people shouting lies at each other about economics and immigration, with research and numbers not really getting a look in. And, more than anything, the outcome seems like a protest vote caused by long-term political disengagement, rather then specifically a genuine anti-EU sentiment.
Contrasting this with the Scottish indyref – after that one, I felt much happier. I was still on the losing side of the argument, but it felt like the arguments has been made and the decision had been taken fairly; even though I didn't agree with the outcome, I didn't feel like it was unfair. I don't have that feeling today.