I think in 40-50 years we'll be better off than if we had remained, it was always going to be a long term thing and not something that can really be measured because "better off" is such a subjective thing. Financially better off? No way, not for decades. But the sense of liberation in not being shackled by EU rules, both current and future, that's an unquantifiable but valuable thing to some.
The EU referendum - like the devolution referendums, like the AV referendum, like the Scottish independence referendums - was unlike a normal Westminster election because it gave the public the chance to shape society over the long term.
With a normal election you know the party who wins only has a few years to prove their worth, this leads to short-termism and an unwillingness to tackle big issues with immediate pain but no benefit until the politicians involved have long since retired. Why do something that will wreck your popularity and have no benefit until the 2050s? There's no incentive.
A referendum gives us the chance to decide a new direction for the country. That's why they should only be called occasionally and why they should be thought through properly. The political establishment had no intention of fulfilling a Leave vote because they wouldn't believe it was possible - if Cameron thought Leave might win, there's no way he'd have called the referendum.
Brexit voters were lied to, sure, not because of bullshit messages written on the side of buses, but by the whole political system which gave the illusion of handing power to the people.
How will things be better, in concrete terms? It'll be a decade probably before anything is really better, and many decades before we're better off overall. It's a long game - if people more generally voted for the long game instead of immediate benefit, maybe the NHS would get sorted and we wouldn't lunge from crisis to crisis regardless of which party is in power.