Cardiff's lead at the top of the table, which was once in double digits, has been eroded away by the chasing pack, and they looked set to suffer a third defeat in four games when Conor Sammon gave Derby the lead with 15 minutes remaining.
But substitute Craig Noone headed home an equaliser from Andrew Taylor's cross to ensure a share of the spoils and keep their advantage over their pursuers at five points.
Cardiff have been made to pay for late-season jitters during previous promotion pushes but Mackay does not believe they are feeling the pressure.
He said: "You have to play the team in front of you. It's not always going to go the way you want it to be, everyone is fighting for everything in this league.
"If there were nerves surely we don't come back at the end, score the goal and nearly get the winner.
"It's about trying to be the most consistent team in the league. We came back and got another point and it's one game less to play."