Do you know, is there any service that gives you permission to get back your sent bitcoin, if wallet is on one network (bitcoin wallet service website) ?
No. The fact that you're even asking means that you're missing the whole point of Bitcoin. Bitcoin transactions are designed to be practically irreversible by nature. It doesn't matter if you're using an online wallet. Once coins are sent to another address, those coins will stay in that address unless that address's owner/controller decides to send it back. No online wallet will issue a chargeback for you because any "recovered funds" will have to come from that wallet's own funds.
The only way you could get them back is if you have a cached version of the website you were on (which I've never heard of) when you made the wallet. I kind of doubt you do so yes they'd gone.
Maybe someone will know how to look into all of the websites you had opened in a certain browser. What browser were you using and on what operating system?
Online address generators usually generate addresses dynamically. Even if the page is cached, the address won't be recovered.