In System Settings -> Colors there is color panel but "calibrate" button is grey and I am unable to calibrate it by myself.
This feature requires a supported color calibration device that looks similar to a webcamera and attaches to the screen to detect the colors
This comment on How do I reset an ICC profile in Ubuntu? states:
sensor device- Example devices - Note though that you MUST check which ones are supported by ArgyllCMS, the software behind "Color" above.