Bricks, Masonry, Asphalt and Concrete - Can a depression be fixed in concrete?

My back patio was poured by the previous owner of this house. However, a puddle of water always forms right at the patio door exit. The slab is about 1/4in from the foundation of the house. Since I know nothing about concrete, I must ask "is it possible that when exiting the back door, a depression was formed from the body weight and high traffic? If that's a pretty stupid question? Please explain what I can do to repair while keeping my knowledge (or lack of) concrete in mind.

The surface may have worn enough to create a puddle, but it has not deflected. It can be repaired easy enough, but it will always look like a patch.

It is highly unlikely that the concrete wore down 1/4 inch under foot traffic. More likely, it was a DIY project gone awry. As Scarborough said, it will always look like a patch if you try to fix it, because it will be a different color and texture. You may try patching it then overlaying the whole patio for a more uniform look. Precisely follow all directions for whatever materials you decide to use. Good luck.

Pecos