I have a road bike with Shimano Ultegra Di2 6870 goupset. Today it was my first long ride with it and alsmost instantly I noticed that the brake pads are not for carbon rims. I tried searching on the internet brake pads for ultegra 6870 but with no luck. Are other ultegra brake pads compatible with my brakes?
According to the Shimano groupset page, both brake options for the Ultegra Di2 6870 groupset (BR-6800, BR-6810) ship with the Shimano R55C4 pads, which are designed for carbon rims.
So more than likely, either the brakes are not setup correctly, or the Shimano pads suck.
If you have carbon rims (with a carbon braking surface) you will need appropriate brake pads, so as not to damage the rims. You do not have to use shimano brake shoes- most (possibly all?) rim brakes will take any brand of shoes.
There is a carbon rim insert for Dura Ace, which might fit the ultegra shoes. However if there are no compatible pads for your brake shoes/ rims, you may have to buy a new set of shoes - not especially pricy, and they will come with pads.