Freddie Sears' equaliser denied the Cumbrians victory after Matty Robson had given them a fourth-minute lead and Dunne was over the moon with his side's second-half display.
"It was end-to-end stuff in the first half but one team dominated in the second half and that was us," he said.
"I was delighted with it and we kept patient and kept passing it. We scored a good goal and we did everything we could do to win the match.
"In the second half, we were absolutely outstanding. We were a bit sloppy at times in the second half with some square passes but what really pleased me was the patience of the players.
"Carlisle started well but I was really disappointed with the way that we started the game. But I haven't got a bad word to say about my players.
"We said at half-time that if we kept passing then we would get opportunities.
"The players are disappointed that they were unable to win the game and we're due a big result with the chances we create."