How do I restore a failed drive from time machine?

I have been successfully backing up my external work drives to a backup drive via Time Machine. This has worked fine in the past and when I have needed to restore a file I could just do into TM, selected the drive and look for the file. Problem is that one of my external drives died overnight and when I go into TM, as the drive is not loaded, TM doesn't give me the option to restore... its as if the external drive backup has suddenly disappeared!

How do I find the backup with no corresponding drive?