Practically no, there is not way. Sorry buddy, a rookie mistake. I assume you didn't actually use an online website and downloaded the code of the website instead and ran it locally. It would be insecure to use an online website hosted by someone else for this. But if by any chance you weren't careful enough and actually used an online website, I would email the owner of the website for a chance he keeps the logs and offer him a reward.
On the website it is written "Open Source JavaScript Client-Side Bitcoin Wallet Generator" so I think the term Client-Side answer to your question unfortunately
There is no way to recover but can you try to restore previous session if you are using firefox..
Open your firefox browser and click the settings below the exit or x and click the restore previous session and maybe you can open the page again including your private keys and public key..
Do this the same in chrome if you are using chrome browser but in history tab.
This one just found and maybe it can help also to recover your lose session
https://lifehacker.com/how-can-i-restore-closed-tabs-after-accidentally-quitti-1452314285After a few research I found the file corresponding to the right Firefox session and I succeed to restore it but bitaddress.org opened to the homepage so that I can generate a new address but not on the previous one
Thanks to your answers anyway.
If somebody else has another idea ...