A second-half own goal from Bradley Orr sent the Bluebirds through to the fourth round and a home tie against Leicester City.
"It was a poor game," Johnson said after the 1-0 defeat at the Cardiff City Stadium.
"It got to the stage where only one goal was going to win it but we didn't really create anything.
"I'm disappointed to be out of the Cup and it's all down to a clever bit of play from Michael Chopra.
"He is brilliant at playing on the edge and he did that all through the game but both teams competed, tackles were fierce although the pitch was a little uneven.
"They had a few more chances towards the end of the game and probably deserved to go through.
"We now have some time to prepare for the league meeting against Cardiff at our ground and we will be ready for them."