Well the 1080P standard represents a resolution of 1920 x1080 but to display HD content there are extra conditions such as a HDCP supporting screen & output device (Blu-Ray player, VGA card, etc.).
You cannot get the full 1920 x 1080 unless you monitor has that resolusion, but even though media player may complain about the HD size, it will usually play it at a reduced size so it wiil fit the screen in the proper proportions