If you play minecraft under Linux in fullscreen mode and some other application gets focus (for example using alt-tab or pressing super key), you can move the mouse on the desktop but you cannot click on anything. It seems that all mouse clicks are still captured by Minecraft. That does not happen in a windows environment.

This problem was shortly discussed here: http://askubuntu.com/questions/682459/what-do-i-do-when-minecraft-in-fullscreen-loses-focus