WPF - PopUp not closed on clicking outside - wpf

Question

I have Custom control which uses control template as shown in below code block. I need to show popup when user left clicks on the control. Once he/she clicks outside the pop up, it should close.
With MouseLeftButtonUp, the pop up is displayed however stays open on clicking outside the popup.
Please note I have set focus on on popup listbox element as soon as pop opens using behaviours:Focus
<ControlTemplate x:Key="ControlWithPopup" TargetType="local:CustomizedControl">
<Border HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
<i:Interaction.Triggers>
<i:EventTrigger EventName="MouseLeftButtonUp">
<ei:ChangePropertyAction
PropertyName="IsDropDownOpen"
TargetObject="{Binding RelativeSource={RelativeSource Mode=TemplatedParent}}"
Value="True" />
</i:EventTrigger>
</i:Interaction.Triggers>
<Grid>
<Popup
x:Name="Popup1"
Width="100"
MinWidth="80"
MaxHeight="300"
AllowsTransparency="true"
IsOpen="{Binding IsDropDownOpen, RelativeSource={RelativeSource Mode=TemplatedParent}, Mode=TwoWay}"
Placement="Center"
PlacementTarget="{Binding RelativeSource={RelativeSource Mode=TemplatedParent}}"
PopupAnimation="Fade"
StaysOpen="False">
<Border
Background="{DynamicResource SomeBackgroundBrush}"
BorderBrush="{DynamicResource SomeBorderBrush}"
BorderThickness="1"
TextElement.Foreground="{DynamicResource SomeFontBrush}">
<ListBox
x:Name="List1"
ItemTemplate="{TemplateBinding DropDownTemplate}"
ItemsSource="{Binding Path=ListSource, RelativeSource={RelativeSource Mode=TemplatedParent}}"
ScrollViewer.CanContentScroll="False"
ScrollViewer.HorizontalScrollBarVisibility="Disabled"
SelectedItem="{Binding Path=SelectedItem, RelativeSource={RelativeSource Mode=TemplatedParent}, Mode=TwoWay}"
Style="{DynamicResource ListBoxNormalStyle}"
VirtualizingPanel.IsVirtualizing="False">
</ListBox>
</Border>
<i:Interaction.Triggers>
<ei:DataTrigger Binding="{Binding IsOpen, ElementName=Popup1}" Value="True">
<behaviours:ScrollIntoCenterView TargetObject="{Binding ElementName=List1}" />
<behaviours:Focus TargetObject="{Binding ElementName=List1}" />
</ei:DataTrigger>
</i:Interaction.Triggers>
</Popup>
<Border
HorizontalAlignment="Stretch"
VerticalAlignment="Stretch"
Background="Transparent"
BorderThickness="1">
<TextBlock
x:Name="Presenter"
HorizontalAlignment="Center"
VerticalAlignment="Center"
FontSize="11"
FontWeight="ExtraBold"
Text="{Binding SelectedValue}" />
</Border>
</Grid>
</Border>
</ControlTemplate>
Note -
- Also note, i dont want to set StayOpen to True due to some reason outside the scope of the problem. I want to achieve it using StayOpen set to False