Searching for installed App by name I used to have a HTC Hero with had it's own search button. When being in the application selection menu I could press the button and then search for an app by typing it's name.
Is there similar way to access apps in Android 4.x without a specific search button?
The Google Search app is able to search the applications on your phone. On 4.1+ this can be done through a Google Now search. On many devices, this is accessible by swiping upwards from the home button in the navigation bar.

When you search for the app on your phone, you can use the bar along the bottom to scroll to "Phone" to search your phone rather than the web.

You can also search "start " so for example if I had an app called (in your case) "Battery", if I typed into the search bar "start battery" it would give me a card showing the app name and icon with a button below saying "Open App"