How to use AlternationIndex in ItemsControls?

I have seen some articles that show how to use AlternationIndex with ListBoxes or ListViews, but I had spent a few hours trying to get alternating background colors on the base ItemsControl class and nothing seems to work. All ListBox samples I saw use ListBoxItem as the target type for the style that sets the background based onAlternationIndex - like this one from MSDN:

<Grid>
    <Grid.Resources>
        <Style x:Key="alternatingWithTriggers" TargetType="{x:Type ListBoxItem}">
            <Setter Property="Background" Value="Blue"/>
            <Setter Property="Foreground" Value="White"/>
            <Style.Triggers>
                <Trigger Property="ListBox.AlternationIndex" Value="1">
                    <Setter Property="Background" Value="CornflowerBlue"/>
                    <Setter Property="Foreground" Value="Black"/>
                </Trigger>
                <Trigger Property="ListBox.AlternationIndex" Value="2">
                    <Setter Property="Background" Value="LightBlue"/>
                    <Setter Property="Foreground" Value="Navy"/>
                </Trigger>
            </Style.Triggers>
        </Style>

    </Grid.Resources>
    <ListBox AlternationCount="3" ItemsSource="{StaticResource data}" 
             ItemContainerStyle="{StaticResource alternatingWithTriggers}">
    </ListBox>
</Grid>

I want to use the ItemsControl because I do not want the selection functionality and I think restyling a ListBox to hide it might not be the best choice.

This is one of the things I was trying:

<DataTemplate DataType