I think you mean you put it in the large cold water cistern rather than the small CH Feed and Expansion tank. Try not to use any hot water until you have cleaned the tank, because this will draw contaminated water into the cylinder.
Draining the tank will be much more effective than just running the tap and letting it get slowly diluted with fresh.
Turn off the supply (or tie up the valve float) and run the *cold* bath tap. With luck it will be fed from the tank and will empty it. Once it has drained (there will be a few inches of water left) untie the float or turn on the supply and stir the water round as it runs through until the scent of inhibitor is gone. This will also allow any fine sediment to wash away and out of the cold tap without getting into the hot cylinder. If you want, you can scoop out the remaining water using a plastic dustpan into a bucket, and sponge the sides and bottom dry. Then let it fill right up again with fresh water. If the cold bath tap is fed from the mains, not the tank, use a hosepipe to syphon out the tank into the bath or other convenient drain.
Get the HW cylinder fully hot, then turn off the boiler and open the *hot* bath tap. The hot water will come out first, because it rises, then the cold water from the tank. Because you have already drained away all the contaminated water from the tank, the cylinder will refill with clean water.
The kitchen tap should, and almost certainly will, be fed from the incoming mains supply, so will be uncontaminated and safe to drink.
There will still be traces of inhibitor, but it will be very dilute, and is not a dangerous chemical anyway. If you want, for example if you have a baby in the house, you can repeat the process, and don't brush your teeth in it for a day or two. By the time you have used a day or so's water, and had a bath, it will have been rinsed away.