Welcome to Android Central!
First, let's make sure we're on the same page. When you say "apps drawer," you're referring to the all apps list, not the homescreen, right? Because deleting icons from the homescreen is simply removing a shortcut, not completely deleting an app.
I don't have an S4, so I don't know how different the app drawer is from the one on my Razr Maxx. How exactly did you delete the icons from the app drawer? If you longpress an icon in the app drawer, you should then see options for "App Info" and "Uninstall," and dragging the icon to an option will execute it. So if you dragged an icon in the app drawer to the Uninstall option, then it should be gone from your phone. I think the S4 also gives you the option to hide an app in the app drawer, so if there's an option for "show hidden," make sure it's checked.
It's possible to Disable apps in the Settings/Apps menu, so if you're still seeing the apps installed but they can't be started, then perhaps you disabled them. Go to Settings/Apps/All, and scroll down all the way to the bottom, which is where Disabled apps are usually listed (although on Android 4.3, the Disabled apps are now a separate list under Settings/Apps). Find the app you might have disabled, select it, then tap "Enable."
Try that for starters.