AWB is OK for daylight scenes but isn't terribly good when encountering mixed light sources and incandescent lighting. This is true for many other DSLRs. That's when I use the manual settings or do a custom WB.
If you need to adjust white balance in PP, you could shoot at a grey card as a test shot and use the grey point eye dropper in Levels in PS to remove colour casts. Of course if the card has a pure black or white swatch, even better as you can set the shadow and highlight as well.
You could also use an Expodisc, which I sometimes use for indoor shots. Accurate and great if you don't want to PP. One caveat - WB will be accurate so long as the lighting condition remains the same. Once the lighting condition changes, you'll need to get the camera to do another custom WB reading.
If you don't want to use/don't have a grey card or Expodisc (or equivalent), you can use Photoshop's Threshold adjustment layers to determine the darkest and lightest parts of the image and neutral grey too, just that it is a little more tedious.