Even after cleaning the image sensor and the glass of the lens you are bound to have spots on your images once in a while. Not removing these in post-processing is a sure sign of an amateur so take the time to clean up these spots.
This is one of the first steps I do in post-processing when in Photoshop. Lightroom 5- the latest version - has an improved spot removal tool, but I still prefer to do my clean up in Photoshop.
In Photoshop, zoom into your image to at least 100%. Scroll through each area of the image looking for imperfections that appear as round discolorations or light gray areas. Use the Elliptical Marque Tool to select the round dust spots. Then, to quickly replace the spot, select Shift-F5. Select Content Aware in the Use drop-down menu, Normal in the Mode drop-down menu, and 100% for the opacity. Select Ctrl-D in Windows or Command-D on the Mac to deselect the area. This feature will automatically adjust the selected area to match the surroundings.