The Google app that looks looks like a little microphone just disappeared from my home screen and I can't find it in the app drawer anymore. Where did it go?
As you have said that the actual app is out of the app drawer, if you press the search button it should come up and you can just tap the mic button.
Also you could make that your double tap home command by going into Settings> Accessibility> and scroll down to the bottom and choose Double tap home launch, make that voice search.