The Bluebirds have been drawn to face fellow npower Championship outfit Crystal Palace in the last four of the competition after Dougie Freedman's side knocked out Manchester United at Old Trafford on Wednesday.
The draw guarantees a second-tier team a place in the showpiece final at Wembley in February and, while Mackay urged caution ahead of the meeting with Palace, he said his side were delighted to have missed the big guns at this stage.
He told the South Wales Echo: "There will be a little bit of euphoria out there at us having missed Liverpool and Manchester City and that's understandable.
"I'd be fibbing if I said I wasn't pleased to be missing out on those bigger clubs and a couple of the biggest in Europe. Playing a team from our own division obviously gives us a better chance of progressing to the final.
"But we do need to calm down a bit. We had a tight game with Palace not very far back at our place. They are a good side with a very good manager."