Why image is not inverted as convex mirror of eye form real image
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. For example, if you start continuously wearing glasses which invert your vision, eventually you will start to see the world upright:
In the 1890s, psychologist George M. Stratton conducted experiments in which he tested the theory of perceptual adaptation. In one experiment, he wore a reversing glasses for 21½ hours over three days, with no change in his vision. After removing the glasses, "normal vision was restored instantaneously and without any disturbance in the natural appearance or position of objects." On a later experiment, Stratton wore the glasses for eight whole days. By day four, the images seen through the instrument were still upside down. However, on day five, images appeared upright until he concentrated on them; then they became inverted again. By having to concentrate on his vision to turn it upside down again, especially when he knew images were hitting his retinas in the opposite orientation as normal, Stratton deduced his brain had reprocessed his vision and adapted to the changes in vision.
Here is an interesting video on the same, from a German experiment in the 1950s:
https://youtu.be/jKUVpBJalNQ