So Android has given us the CardView to replicate such behavior. It provides a View with a rounded corners, that applies a drop shadow. You will probably also want to look at the #setCardElevation()method.
You can add the CardView Library to your Gradle Project:
compile 'com.android.support:cardview-v7:21.0.+'
The CardView will use the Lollipop implementation to do this if it's available (as Lollipops shadows are better), otherwise it will replicate it as best as it can.
Here is a sample:
<android.support.v7.widget.CardView xmlns:android="http://schemas.android.com/apk/res/android" xmlns:card_view="http://schemas.android.com/apk/res-auto" android:layout_width="wrap_content" android:layout_height="wrap_content" card_view:cardBackgroundColor="#ffd9d9d9" card_view:cardCornerRadius="2dp" android:layout_margin="6dp" card_view:cardElevation="6dp"> <TextView android:id="@+id/text" android:layout_width="wrap_content" android:layout_height="wrap_content" android:paddingTop="8.5dp" android:paddingBottom="8.5dp" android:paddingLeft="12dp" android:paddingRight="12dp" android:textColor="#de000000" android:fontFamily="sans-serif-medium" android:text="NORMAL" /> </android.support.v7.widget.CardView>
The above code running on 5.0: 
The above code running on 4.4.4: 
It looks like there is a discrepancy in the fonts, as in the sans-serif-medium has a different font weight or isn't supported on 4.4.4, but that can be easily fixed by including the latest version of Roboto and overriding the fonts on the TextViews.
The material documentation you post point to an an "Elevated Button". CardView's are how we make "Elevated" anything.
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