Say I'm playing my game and I press enter, which does nothing while I'm in game. As soon as I pause it, that enter press get's registered and selects the first thing in the menu.
Are you saying this happens already, or that you want this to happen?
If it already happens, then it's probably a bug with Slick and/or your game's codebase.
If you want
it to happen; then you just need to listen for key events and store them in an array list or something. When the game is paused, fire off all your stored key events, and clear the list for the next time around.