Searching for file within Time Capsule Mavericks OSX 10.9.5.
I need to locate a file in the Time Capsule.
I can navigate into the directory I want to search in, and using OSX find, I can "search" for a file that is right there and there are no results.

For example navigate to directory Website containing two or three files including index.php and search for "index.php" yields nothing.

I think that I'm not actually navigating to a directory, but that the OS is displaying a virtual directory based on the Time Capsule database.

How does one search for a file within Time Capsule backups?
Searching a TimeMachine backup is tricky - for one thing Spotlight has not indexed the backup (do not tell Spotlight to do this - you will be in for a world of hurt)

Second, you are sort of correct about about TimeMachine being virtual.  what it really is a hundreds of symlinks that link about in all kinds of crazy ways.

Your best bet, is to mount the volume using TimeMachine and recover the file using the interface Apple has provided.

If you are not going to do that, then hopefully you know where the file should be on the original system, and you should navigate to latest/path/to/file.html  where "latest" is the name of one of the directories in at the root of the TimeMachine archive.  Really it is...  If you know what date you want the file from, you could use that date in place of "latest"