With full Auto and with no EXIF data we have no way of knowing ISO setting, aperture or shutter speed. Without knowing aperture setting, focus distance and focal length we cannot determine depth of field (DoF).
However, if you get those values from your camera or from the EXIF in the image file and go to http://www.dofmaster.com
, you can come up with the DoF.
Anyway, the root cause of the lack of sharpness in the background is that the DoF is too shallow. However, these are not defects in the system - they are the symptoms of the physics of the situation. In order to get a sharper background (if that is what you really want), you need more DoF, which can be attained by moving to Tv mode, using a shutter speed of about 1/focal length (Ex. with focal length = 125, use 1/125" shutter speed).
The result will be an aperture that is more stopped down, giving a greater DoF. If that is still not good enough, you can bone up on hyperfocal distance and find out how to set up the shot using the hyperfocal distance in order to get the best compromise between near and far items of interest.
If, after all that, you still need a greater DoF, you will have to set the ISO higher and shoot it one more time.