City were cruising when 2 - 0 up at half time but went on to lose the game 3 - 2.
"We committed suicide by gifting Palace two penalties. The first one, one of our players raised his arm. With the other one Helguson made a rash challenge," Mackay said.
"I was disappointed today and delighted at Millwall. If we don't give two penalties away we would have sat top of the table tonight.
"I don't have any qualms with the penalty decisions. In the first half we scored two good goals and the third chance, nine times out of 10 Bellamy would have taken that. But we gifted them two penalties."
The happier man was Palace manager Dougie Freedman.
"As manager it was the best comeback," Freedman said. "I don't think we deserved to be two down. To show the character and energy we did, it was a correct result.
"If you were watching the game, you saw we didn't deserve to be down. We played with fantastic approach play, with crosses.
"In the second half, the shots were coming off and we were causing them a lot of problems. Cardiff are a good side and we've stood up to good challenges with them and Forest this week [1-1 draw on Tuesday]."
Source: FOOTYMAD
