I get that this is just a small part of a much larger issue, but as a concrete suggestion to a concrete example, there are couple of ways to achieve this: a) they've got a very sophisticated platform of their own, b) they're using one from elsewhere (such as Shopify) or c) for that price they install an out-of-the-box e-commerce solution, do minimal work on it and that's it.
Not trying to be depressing here, but if an out-of-the-box solution really what the client wants and needs, that's what they should get. If you want to compete with companies like that and offer your services for clients with such needs, I'd suggest looking into existing solutions -- preferably ones provided as hosted services.
If a client wants something entirely customised to their needs, I can assure you that no one can provide it for 399€. Not unless they're counting on making profit from the monthly fees in a long run, in which case the price of the project itself can be much lower than what it costs for them to build. I still very much doubt that anyone would do a >10K€ project for <500€, that's just too much of a stretch.
The key here is that uniqueness, authenticity, adhering to specific requirements -- and generally speaking any work that requires involvement of a real person with real ideas -- cost. You can't get all that for couple of hundred euros. For the clients that appreciate this, a bulk product just isn't going to cut it. For those who don't, it's probably pointless to even try to sell it.
Out of all the great posts on this thread already, I really liked what @yellowled said about "saving them time, effort and nerves". That's one heck of USP (as explained by @totoff) if you do (and communicate) it right. As another concrete example, we've been involved in projects that have literally cut a weeks worth of manual work to an hour or so of waiting for a background task to run. It'd be pretty hard for a client to not value that.
I'm sorry that things are difficult for you and really think you're right when you say that people don't appreciate craftsmanship much these days. It's a sad thing, but all I can say is that you'll have to either find a way to provide good quality with minimal effort (out-of-the-box services) or find a way to attract clients that do appreciate this. I know that neither is really an easy way out, though..
(For the record, I work for a company that provides web-based solutions ranging from the most basic self-service platforms for small companies and individuals to entirely custom-built ones for large corporations, cities/municipalities etc. For some clients we handle everything from content to marketing and some prefer to do these things themselves. There are clients for all of our products and none of them is perfect match for all of our clients.)