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"
Try google gesturesearch using this you can not only search for an application but also contacts,music and bookmarks.
This has a cool feature that you can use natural hand writing to type the app name and keypad is not needed.
There is an option in Google Search / Now settings to allow you to search through apps as well as web (Go to Google Now settings, there you'll see phone search, open it and tick Apps)