I figured this out the other day by accident. On your phone go into the Play Store and select My Apps. There are two tabs at the top, INSTALLED and ALL, tap ALL. You will see a list of all the apps you have downloaded. Apps which are no longer installed have an "X" next to them on the right side..
Press and hold the app you want removed from the list; it will turn blue. You can select other apps for removal from the list by tapping the corresponding line. When you are finished, tap the "X" at the very top right of the screen (to the left of the X, it'll show how many apps you have selected; also, don't tap the check mark on the far left of the screen, or else you'll have to re-select everything), and you'll get a popup to confirm deletion.
This method will not work on installed apps, only apps that have been installed then removed.
I'm not sure if this can be done on a PC, but it's pretty quick on the phone.
EDIT: With the recent Play Store updates, Google changed the way downloaded apps that are not installed appear on the ALL tab. They now have an "X" instead of the Circle Slash. I also edited my post a little to reflect the new behavior of the Play Store. Again, this method will not work on pre-installed apps.