You should make sure your game doesn't block features that belong to other programs or the operating system. Task Manager is an essential component of Windows and Linux to let the user close an application that's not responding or consuming too much CPU / RAM.
Altering the behavior of the quit function of your game can create the psychological effect you're looking for. As an example, in Red Balloon of Happiness there is a point when the normal quit is disabled so the player needs to use Task Manager.