Do you imagine how many websites are there, used daily by hundreds of thousands of people who don't care that the website they use is poorly written?
Even better, do you imagine how many websites are there, not only poorly written, but also unsecured, unusable, but still used by many people?
Your website is functional and works well? So release it. An end user doesn't care about the quality of your code. If the website doesn't crash every minute, doesn't make the user feel stupid or uncomfortable, or doesn't suck too much, there is nothing to worry about.
If have to worry about in several cases, which doesn't seem yours:
When the website was done for your customer, and you were payed for it. A customer may not be able to make a difference between a high quality code which works and a code that suck but works, but if one day this customer asks some other developers what they think about the code you made, you have strong chances to lose this customer forever.
When you seriously intend:
to enlarge, promote and modify the website. If half of daily visitors ask for a feature, and you cannot implement it, because it requires to rewrite the whole source code correctly, well, there will be a problem.
to share or sell your source code. In a first case, your reputation may be affected if other developers see a very low quality code. In a second case, the buyers will expect some quality, and will be disappointed.
to invite somebody to work with you on the source code to enhance the website.
Last advice: don't try to make things perfect. Release first, then do it. By releasing a website, you will receive feedback sooner. It means that you will be able to implement some modifications according to this feedback sooner too. Thus, the quality of your next version of the website will be higher.