You will have no problems landing small carp on a 2.75 tc rod,it is how you play them that counts,having the clutch set right and so on,i have caught a Gudgeon on my 3lb tc rod and never got a hook pull,it is a different matter going for big carp on a low tc rod,if the water you are fishing have small (up to 10lb carp) only then you could go down (if you have one) to a 1.75 to be better off but if not you will still hold with that rod,just play it right and job done.
Stan.