That makes no sense. You use a password manager so you don't need to manage the passwords. If you don't like the concept of having passwords at all then use a stateless, hash-based password generator instead.

How does one integrate that with Facebook or Google or Nameasite?

A browser extension could be made pretty easily. If you have a terminal open, do `echo mymasterpassword facebook.com | shasum -a 256 | pbcopy`.