The Bluebirds had managed to edge themselves in front at Stamford Bridge, with Jordon Mutch profiting from some slack defending to break the deadlock.
The tide was, however, to turn back in Chelsea's favour on 33 minutes when David Marshall went to bounce the ball inside his penalty area, only to see Samuel Eto'o nick it away and provide the platform for the Blues to restore parity.
Jose Mourinho's men ended up putting a comprehensive slant on the final scoreline with a late flurry of goals, but Mackay believes his side were robbed of the opportunity to make the match more of a spectacle by poor officiating.
He told Sky Sports: "I've been in to see the referee for clarification and it appears that he has got it horribly wrong. Our goalkeeper bounced the ball. He saw Eto'o standing next to him and he bounced the ball.
"I asked the referee for clarification on what he thought happened for the first goal. The linesman thought that the goalkeeper dropped the ball. So I said, 'If he bounced it?' And he said, 'If he bounced it, it's a foul, but we think he dropped it and the ball was in open play'.
"Well, you can look at the pictures and see that it was clearly bounced. It should have been a foul, it then gives them a goal and we go in at half-time level rather than 1-0 up. It's a horrendous error."
Up until that point, Mackay felt Cardiff had been holding their own and providing an attacking threat.
He added: "We had a couple of breaks ourselves and a fantastic free-kick which Peter Odemwingie has touched on and (Petr) Cech has pulled it out of the top corner to go 2-0.
"At that point, little things change games massively, especially against a top team like Chelsea."