You can buy a replacement online from Apple or at an Apple store.
Yeah, it's always a good idea for networked devices that require configuration to have a web interface for configuring them. The Apple TV doesn't. I've complained about that from the start, as entering long passwords through the on-screen keyboard is a royal pain. If there were a web interface, it would be a simple matter of connecting temporarily to my wired network and then copy and paste.
If you have a Harmony or other updateable remote, you may be able to configure it as an Apple remote, which is just an ordinary IR remote. Otherwise, you'll have to buy an Apple remote.