Goalkeeper Tom Heaton was the Bluebirds' hero, saving two Palace spot-kicks after Anthony Gardner's own goal levelled the tie 1-1 on aggregate.
The Welsh outfit's trip to next month's Wembley showpiece was then secured when Jonathan Parr skied his effort from 12 yards high and wide.
For Mackay the win justified the effort and commitment put in by his players, who dominated their guests for much of the match and spent almost the whole of extra time camped in Palace territory after Paddy McCarthy was sent off late in the second half.
He said: "I was delighted with the way we went about our business. I was very proud of them. We started the game on fire.
"The early goal calmed everything down and allowed us to probe. It calmed the crowd down and let them attack the game. It was a fine night's work.
"When Aron Gunnarsson hit the bar with the last header of the tie you do think it may be one of those evenings.
"It's obviously a lottery when it goes to penalty kicks but I had great belief in their ability and spirit to keep going.
"I'm delighted for the group of players, I'm delighted for the football club tonight.
"You look all the way through the competition, from Oxford when we had 10 players missing through international duty to tonight where it was always going to be tough, we've shown character and spirit.
"Tonight another little bit of history has been made for this football club.
"It's terrific for everyone at the football club and everyone should embrace it."
Mackay reserved special praise for Heaton, who made the most of his moment in spotlight to capture the headlines.
Heaton has played second fiddle to first-choice stopper David Marshall for much of Cardiff's league campaign but has started six of the Bluebirds' seven Carling Cup clashes.
And Mackay was pleased the former Manchester United man, who was blamed for Palace's goal in the first leg at Selhurst Park a fortnight ago, took his chance once again.
"He knew this was his competition, I told him that all the way through," he said.
"He probably had a little bit of criticism after the goal in the first leg but I'm delighted for him tonight.
"He's someone who's got great character about him and he's one of the leaders in the dressing room and he thoroughly deserves the accolades tonight."
Palace boss Dougie Freedman expressed his pride at the way his players dealt with the dismissal of McCarthy to force the match to penalties.
Freedman was left devastated after Sean Scannell and Jermaine Easter were thwarted from the spot by Heaton before Parr blazed over, but he paid tribute to the 'never-say-die' mentality evident amongst his matchday squad.
He said: "It was a fantastic physical effort. I felt we were asked a lot of questions which we answered. We dug in and I felt we grew into the game.
"The sending-off was disappointing but the response - you could not ask much more as a manager.
"The pride we've shown and the desire to work hard for each other and the commitment to each other was second to none and I'm really proud of that.
"I'm disappointed short-term, but long-term I think we can take a lot from that. We can take a lot from the challenge and the way we responded to it.
"I thought we were prepared and up for the challenge and we came close tonight.
"I think we won a lot of hearts tonight. It was a great cup tie and overall it was a very well-played game. It just wasn't to be.
"With the physical output we had to put out in the game, it's difficult to compose yourself and slot the penalties."