The win marks the first time that Birmingham have reached the last 16 since they won the Cup in 2011, which pleases Clark.
"I'm absolutely delighted," Clark told the press. "I think to win a game like that against the quality of opposition we're up against is very satisfying.
"Not only are Swansea the holders but I said before the game that I felt it was the hardest tie we could have got outside the so-called top six, a club that's on the up in everything that they do. Even though they made changes I don't think it affects them as they've got a philosophy that runs through the club.
"I hope the players gain confidence from the victory. I can see the players are gaining confidence game-by-game, there were some terrific individual performances out there."
Birmingham will host Stoke City in the fourth round.