Assuming you haven't changed the Button's template, the default control template for Button uses the VisualStateManager to overlay a white rectangle with 50% transparency over whatever content you have in the button. This should give the content a "washed out" look.
If you have replaced the template, you would need to replicate this behavior. Silverlight doesn't have Style triggers so you'll need to use the VisualStateManager. Do you have Expression Blend? If so you can see the default control template by dragging a button onto the designer, right click -> edit template -> edit a copy.
EDIT
I've included the default control template for Button as extracted by Blend. Take note of the Disabled state in the VisualStateManager.
<ControlTemplate TargetType="Button">
<Grid>
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
<VisualState x:Name="Normal"/>
<VisualState x:Name="MouseOver">
<Storyboard>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="BackgroundAnimation" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value="1"/>
</DoubleAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#F2FFFFFF"/>
</ColorAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[2].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#CCFFFFFF"/>
</ColorAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[3].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#7FFFFFFF"/>
</ColorAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="Pressed">
<Storyboard>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="Background" Storyboard.TargetProperty="(Border.Background).(SolidColorBrush.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#FF6DBDD1"/>
</ColorAnimationUsingKeyFrames>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="BackgroundAnimation" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value="1"/>
</DoubleAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[0].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#D8FFFFFF"/>
</ColorAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#C6FFFFFF"/>
</ColorAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[2].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#8CFFFFFF"/>
</ColorAnimationUsingKeyFrames>
<ColorAnimationUsingKeyFrames Storyboard.TargetName="BackgroundGradient" Storyboard.TargetProperty="(Rectangle.Fill).(GradientBrush.GradientStops)[3].(GradientStop.Color)">
<SplineColorKeyFrame KeyTime="0" Value="#3FFFFFFF"/>
</ColorAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="Disabled">
<Storyboard>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="DisabledVisualElement" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value=".55"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualState x:Name="Focused">
<Storyboard>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="FocusVisualElement" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value="1"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="Unfocused"/>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Border
x:Name="Background"
Background="White"
BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
CornerRadius="3">
<Grid Margin="1" Background="{TemplateBinding Background}">
<Border x:Name="BackgroundAnimation" Opacity="0" Background="#FF448DCA"/>
<Rectangle x:Name="BackgroundGradient">
<Rectangle.Fill>
<LinearGradientBrush EndPoint=".7,1" StartPoint=".7,0">
<GradientStop Color="#FFFFFFFF" Offset="0"/>
<GradientStop Color="#F9FFFFFF" Offset="0.375"/>
<GradientStop Color="#E5FFFFFF" Offset="0.625"/>
<GradientStop Color="#C6FFFFFF" Offset="1"/>
</LinearGradientBrush>
</Rectangle.Fill>
</Rectangle>
</Grid>
</Border>
<ContentPresenter
x:Name="contentPresenter"
HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}"
Margin="{TemplateBinding Padding}"
VerticalAlignment="{TemplateBinding VerticalContentAlignment}"
Content="{TemplateBinding Content}"
ContentTemplate="{TemplateBinding ContentTemplate}"/>
<Rectangle
x:Name="DisabledVisualElement"
Fill="#FFFFFFFF"
RadiusX="3"
RadiusY="3"
IsHitTestVisible="false"
Opacity="0"/>
<Rectangle
x:Name="FocusVisualElement"
Stroke="#FF6DBDD1"
StrokeThickness="1"
RadiusX="2"
RadiusY="2"
Margin="1"
IsHitTestVisible="false"
Opacity="0"/>
</Grid>
</ControlTemplate>