Once you tab into the search that brings up the search pane, there's no way through the keyboard to get out. Several clients have raised this issue since it is significantly impacting some of their end users. This feature request is to either add a way to deal with the keyboard trap with the new Quick Search Panel, or at the very least disable the new search.
You can use custom html to target the search input and then add a tabindex value of -1 to remove it from the list of items you can tab into. For example, you could do this via jQuery with the following code:
This will enable you to move past the search field with using only the keyboard. Then you can just open it manually with the '/' keyboard shortcut if need be.