The home side scored with their only shot on target - a fantastic finish by the hard-working Alan Judge in the first half - to close the gap on the top six.
However, County were grateful to a stunning display by keeper Bartosz Bialkowski who pulled off a string of terrific saves to deny Carlisle.
Kiwomya said: "Draws are no good to us anymore if we want to get to the top six. We've played better at Stevenage and lost and at Tranmere on Tuesday and only drew but that happens in football.
"They came with a game plan and pressed us high. At half-time we said they are pressing us high and we are going to have to play a bit longer and a bit quicker.
"I said to them these are the games that are the horrible games where we have to grind out the result. We can't play well all the time so if we cannot play well and still get victories that has got to be good.
"At this stage of the season and when the pitch is not great, you've got to play the pitch sometimes. I'm not going to criticise the players as some of them are tired and you could see that at times."