It was an incomplete read. You put him on the bottom of a range that was best for you. You needed to take it a step further and include Kx so it would look something like this.
AA**, AK**, KK**, KQ**, KJ**, KT*, K9, K8**, K7, K6, K5, K4, K3, K2**
** You are crushed
I know, this is over simplified - point is your range was way too narrow for a flop.
And by the way - you said you thought he could have K3 or K8??? Helloo??? You got close - remember to follow through.
Don't know what stage of the tourney this was, but if early this was a bad call - ne need to risk your life on a T kicker just yet.