As I think I touched on in another of your threads Carl, generally when you shade a colour you want to keep the hue the same - when painted shadows look wrong the hue having changed in one of the major culprits.
The swatch you've posted is red in hue, so if this is reasonably representative of the real colour that's what you want to aim for in the hue of the shadows. Burnt Umber is orange in hue generally. If you like how this worked that's all that matters but be aware that this is a change of hue; it would be normal for the hue to still be red, just darker (and a little duller).
The simplest way of doing this might be to use a little Cad Red (or another mid-red) + a touch of black.
Einion