"It was very disappointing, as we let ourselves and our fans down," said Cardiff manager Dave Jones.
"It was our worst performance of the season, and I have no complaints about losing.
"We didn't deserve to win the game, and players shouldn't be jumping into the tackle, but that is another set-piece which has let us down.
"We lost our discipline, and I have no complaints about the other bookings, but I think Stephen McPhail actually won the ball when he received his second yellow card.
"Fair play to Swansea, but now we look back to the league this Saturday, and this defeat may make us more determined. Both sides tried to play, but Swansea were a little better than us."
"I thought it was a deserved victory, and the atmosphere has made it a very special day," said Swansea boss Roberto Martinez.
"The first 20 minutes, Cardiff made it difficult for us, but then we kept hold of the ball, and it was a good level of performance from all my players.
"We knew how important it was to our fans to get this victory, and they certainly helped us with their massive support.
"This night will be remembered for a long time, as the game fulfilled all expectations. It was a magnificent derby and a good advertisement for Welsh football."