Those spots are on the sensor. It is not possible for the camera to focus that well on any particles insides the lens.
This is the same concept that applies when trying to shoot through a fence... if you get your camera lens very close to the fence and take the shot, the fence doesn't show up in your image -- it blurs out to almost nothing. In order for anything to show up, it needs to be located close to a focus plane (in other words... it needs to be on the sensor.)
After cleaning your sensor, attach a lens, point at a plain white wall or ceiling (something with no contrast -- even a plain blue sky would work), pick a reasonably high f-stop (e.g. f/16) and take a shot (you don't need to focus the lens -- in fact it's almost better if you deliberately don't focus the lens.) It should be very easy to spot any dust particles in the shot.
Some Nikon bodies had issues with oil splatter. Owners could clean the sensor, verify it is spotless, but within a handful of shots new spots would start showing up again. What camera body are you using?