If you bought a product from someone and then immediately got told that one of the main reasons you bought it wasn't in fact true you would want a refund, or at least some sort of compensation. The company selling it would likely suffer financial penalties and in certain cases people involved will serve time in prison. But when it comes to voting it is apparently fine to mislead and lie to manipulate people into choosing a certain way. You could equally argue that this vote has only further perpetuated the idea that politicians can say whatever they want to get the votes and then the day after admit that they lied but it is too late now for anyone to do anything because the votes were cast.

Democracy is founded on the idea that your vote matters.

How can you say that your vote really matters if the thing you voted for is actually revealed to be different the day after you voted? Winning by obtaining votes through manipulation, scaremongering and lying isn't what democracy is meant to be. We voted the politicians in to make these sort of decisions and at the end of the day a public vote on this matter was a terrible idea. If they gave us the option to vote on how much income tax you wanted and the quality of the NHS, schools and roads then people would vote for zero tax and perfect quality services, but that is fundamentally impossible.

(since it was only advisory)

If it's only advisory then it wouldn't go against democracy at all. Politicians often have to do things that are against what the majority of the public want. Raising the age of retirement, increasing VAT, raising tuition fees, reducing NHS funding to name a few. You could argue that every time the government made a decision like this, they were going against democracy by this logic.

That the decision to make a practically irreversible change to our country won by such a small majority after the immediate admission of the Brexit leaders that they had lied and the number of people saying they regret their vote, is a good reason not to proceed with the exit from the EU.