Measure power at an idle state. The idle state can be many things. This needs to be decided by you:
The board operating when the FPGA is not programmed (no bitstream loaded).
FPGA loaded, but you hold down the reset for the logic.
Place the FPGA in some kind of suspended state (sleep mode).
Now that you have your reference power measurement, measure the power with your design running fully. Subtract one from the other, and you will have a result which is close to what you are searching for (The board may consume differently, at each idle state, than it would have been when running normally with your design).