There's a back story here which we don't know - learn as much as you can from it.
- If the potential customer directly asked for the app, learn to take a deposit of some proportion of the cost of the work
- If not, do some basic investigation that there's a wider market
- Did you simply misunderstand a mere expression of interest as a buying signal?
Have you asked the potential customer why he is not interested? Something significant may have happened in his business whilst you were developing it - without any contract - tough.
Now, depending on how specialised and unique to your customer your app is, you may have an MVP (Minimum Viable Product). You may be able to market it and gauge interest in the product. That could be as simple as throwing up a web page and driving some traffic via adwords to see if you can make a sale or three or get some email sign ups. You may have to do more traditional marketing (very much depending on target market and type of product).
As to whether you should, only you know how specific the product currently is, costs to make it suitable for a general market, and potential sales. Was it a week's work or months? So only you can say if it's worth taking further, or just to be written off to experience.
Have a google on "customer discovery" and a look at http://steveblank.com for some background reading.