Heidar Helguson's close-range header gave City an early lead at Pride Park, but the hosts equalised through Theo Robinson following Craig Noone's dismissal for two yellow cards in the space of three second-half minutes.
Derby arguably deserved to take all three points, but a Cardiff backline featuring two teenagers - Joe Ralls and Ben Nugent - held out to secure a share of the spoils.
That was enough to please Mackay, who oversaw a 2-1 victory at Barnsley on Saturday and is hoping to welcome back four senior players for the weekend visit of struggling Sheffield Wednesday.
"We've been up in Yorkshire and Derbyshire and picked up four points out of six with a real patched-up group," he said.
"I'm delighted to be bringing (Kevin) McNaughton, (Andrew) Taylor, (Ben) Turner and (Don) Cowie back in, hopefully for Sunday.
"We really ended up quite threadbare tonight, but I'm very proud of the group. We stay top and we stay top scorers in the division as well, which is important."
Although he had no complaints about the decision, Mackay rued the red card picked up by Noone, who was booked for two clumsy challenges in quick succession.
"I was really delighted up to 60 minutes and think we could have gone on and won the game by more," said the Cardiff boss.
"The sending-off then changes that and means you have to be dogged and resilient.
"We were playing a good team here, a team that have only lost once at home and have won their last three games (at Pride Park) and scored nine goals, so it was always going to be a tough game.
"But I thought up to that point (the red card) it was a calm, professional performance and it finished that way.
"I was delighted by the way we made sure we professionally saw the game out."