Stanley boss John Coleman admitted Carlisle deserved their victory in the 1-0 win at Brunton Park.
Derek Asamoah's 20th minute goal separated the sides.
Coleman said: "I am disappointed. Carlisle deserved to win the game and we can't argue with that.
"I feared for us this week to be honest and sometimes as a manager you just smell it.
"They were better than us in every department. I guess the small crumb of comfort is that you can see how far we have come in that they are time-wasting for 70 minutes of the game. It's the only crumb of comfort in that we are starting to earn more respect from teams."
He continued: "We are better than we have shown in the last two games as we haven't really troubled their keeper. We haven't created enough opportunities against a team who are leaking goals for fun.
"They were up for the game and we weren't so that's disappointing. On the day Carlisle were far better than us but pound for pound, they are not.
"They have outfought us and that's hard to take from my point of view."