"It was a battle throughout the game but we kept going," said Dave Jones, who watched the match from the stands after being given a two-match suspension.
"In the second half it looked like two very tired teams out there and although we missed a couple of chances late on, we stuck to the task.
"It was a very important game to win today as they are a very good side and now we need the break from league football as there are a lot of tired bodies in the dressing room."
Plymouth boss Paul Sturrock though his players struggled
"It seemed to be a game too far for some of my players," he said.
"Cardiff started well, scored the goal and it turned out to be difficult for us chasing the game as it seemed to sap our strength.
"Everybody seems able to beat everyone else in this division and if I can dabble in the transfer market we can maybe freshen things up as we need more competition for places.
"It is a very difficult division and my aim is to stay in the race for the play offs until I can strengthen."