It’s all done by the brain.
The eye is just a sensor. Making sense of what is sensed is the job of the processor - the brain. In addition to inverting the image on the retina, the brain is also able to combine the images from the two eyes to give us the perception of depth.
In fact, this processing is not passive. That is, the brain does not just take the image from the eye and invert it. If the input to the eye is altered over a sufficiently long period of time, the brain is able to compensate for it. This is known as perceptual adaptation
you can learn more about perceptual adaptation
from the link 