He said: "Derby came here and deserved to go away with the three points because we weren't consistent enough in our decision-making and in the way we went about our job today.
"Usually the person on the ball makes the correct decisions in the main but I thought we had too many people today who were not making the right decisions when they had the ball in terms of what they were going to do with it."
Referee Keith Stroud booked seven players, including five for the home side, in a match of few chances.
Mackay said: "I know the referee has given out seven red cards in 12 games this season and I can see why.
"Some bookings I truly thought were strange decisions."
Derby boss Nigel Clough was happy to finally see his side win away.
Clough said: "It's been a long, long wait for it (a first away win). but for the three performances we've put in this week we've deserved to win at least one of those games.
"We could have easily beaten West Brom (drew 2-2), could have won at Preston (drew 0-0), but we got our victory here. The level of the three performances has been excellent.
"We look solid, we restricted an extremely good attacking side to very few opportunities and then we looked relatively dangerous ourselves, certainly compared to what we have done in the previous away games.
"We just felt if we kept it at 0-0, put the ball in the right areas then on a very difficult surface we might just get some reward today."