No never admit liability or agree that you were at fault, even if you think you caused the accident. Just stick to the facts and leave opinions out. Any — in the heat — of the moment comments could come back to bite at a later date after the event of a car accident. You could also invalidate your insurance policy by admitting liability (read the small print on your insurance documents).
If the other person admits liability, still remain cautious as they could change their mind later and deny responsibility.