The Bluebirds, who remain seven points clear at the Championship summit, were undone by two penalties at London Road, both of which were scored by Grant McCann.
Mackay branded both decisions `poor' and accused Posh hitman Dwight Gayle of diving.
Mackay said: "I spoke to the referee at half-time as I was concerned their lad Gayle was going down almost every time one of our players went near him.
"The crowd seemed desperate to see penalties given and I guess they got their wish in the end.
"I have watched the two penalty decisions several times. Don (Cowie) won the ball for the first one and Gayle was on the way down before Matt (Connolly) had even challenged him for the second one.
"Both are poor decisions and I'm hugely disappointed to leave here with nothing. My goalkeeper has had nothing do either side of the penalties.
"We also had a strong handball shout of our own that the referee didn't even give a second thought to. I find that incredible.
"But my players have shown terrific character to be top of the league for four months and bounce back from any setbacks they have suffered. I have no doubt they will do that again in our eight remaining games."