Thank you for feedback.
Removing the head was not that hard since there the 105 5800 has some covers on the bottom side of the shifter body as well as where the cable goes to the housing.
After removing the cable head I shifted many times and removed any pieces of cable left there.
I thought I did it diligently, but today when riding to work after some 2 miles, click to move to smaller cog and ... nothing?
Stopped and pulled the cable manually and all starting working again.

Will open it tonight and see (try) if some small piece is lost there....