As specified by the top answer, I used the following in the code behind the button control.
Private Sub btnClose_Click()
Unload Me
End Sub
In doing so, it will not attempt to unload a control, but rather will unload the user form where the button control resides. The "Me" keyword refers to the user form object even when called from a control on the user form. If you are getting errors with this technique, there are a couple of possible reasons.
You could be entering the code in the wrong place (such as a separate module)
You might be using an older version of Office. I'm using Office 2013. I've noticed that VBA changes over time.
From my experience, the use of the the DoCmd.... method is more specific to the macro features in MS Access, but not commonly used in Excel VBA.
Under normal (out of the box) conditions, the code above should work just fine.