"I'm absolutely not taking anything away from Bristol's performance but as far as we're concerned we gave away bad ball in poor areas.
"It's certainly not like us. If we give them the ball in poor areas then you're going to get punished by good teams."
"We just have to stop making basic errors like that," added Mackay. "It's not something that's been regular from my team.
"Defensively we've been tight as a team, but you have days like that when you give away ball between your 18-yard line and the halfway line - poor areas. You expect to be punished and that's what happened."
"Considering the lack of game time they've had, both of them did well," said Mackay of the newcomers Tommy Smith and Matt Connolly.
"They showed exactly why I bought them. Tommy in the first half got into some great positions and on another day those shots can go in.
"Barring the misplaced pass for the fourth goal, Connolly had an excellent debut."
Bristol City manager Derek McInnes said
'We are getting goals from the middle of the park, which we didn't do last season and now have some great options up front.
'With Sam and Steve on board, we have a lot of different strikers, who pose threats in various ways. All the clubs I have been at, who were successful, had good strength in depth when it came to strikers.
'We will not get carried away because we know how quickly things can change, but all credit to the players for the work they have put in so far.'