Liam Noble grabbed a goal in each half to give the Cumbrians victory in the League One encounter at the Keepmoat Stadium, but Rovers remain in a strong position for automatic promotion after both Swindon and Sheffield United were also beaten.
Flynn, whose team are seven points clear of third, was not too concerned with Tuesday's performance and challenged his players to bounce back with a victory at the weekend.
"We started the game strongly but all credit to Carlisle for making it difficult for us," he said.
"They were very energetic and stopped us playing before grabbing a goal from a deflection and then the second one put a different complexion on the game.
"We started the second half brightly as well but it just wasn't our night.
"I'm not just writing it off like that but it's not the end of the world and the league table will look the same in the morning because nothing has changed with two of our rivals losing.
"People have been getting excited about our prospects of winning the league but we've got to do the job first.
"After the game, the players were deflated but I think there will be a response at Crewe on Saturday - no doubt about that."