You can't restore a Parallels Desktop installation from Time Machine if you aren't doing a full restore, Parallels installs files in various places with the added problem that these places might vary with OS X version. Best approach is to do a fresh install.
However, this is different for VMs, If your VM(s) are not Bootcamp based you can restore them from a Time Machine backup, if Parallels was configured to back them up. Each VM completely contained in a .pvm file (actually a folder/package), typically located in /Users/<username>/Documents/Parallels/.