On the Google Play Store app, swipe in from the left, tap My Apps, then All. You have to select each app to remove from the list by tapping the little X in the upper right hand corner. There's no way to do this in the Google Play Store web interface. The All Apps section is a record of all apps you've installed on that account, so Google doesn't let you completely erase an app from that list.
One minor nitpicky thing--"Android Market" is a very outdated term. It's been Google Play Store for a while.