Heidar Helguson's ninth goal of the season put the Bluebirds ahead before Darius Henderson was sent off for elbowing the veteran striker, and substitute Rudy Gestede sealed the win with his second-half brace.
Henderson missed Forest's best opportunity when he failed to convert from close range, while Lewis McGugan had an effort ruled out for a foul on Aron Gunnarsson as they dropped out of the play-off places and saw their 10-match unbeaten run ended.
Watford's defeat at Peterborough means npower Championship leaders Cardiff are now 12 points clear of the third-placed Hornets with four games remaining.
A draw against Charlton on Tuesday will be enough to secure the Welsh club's return to the top flight after a 51-year absence.
Mackay hailed the performance as one of the best of the campaign, but insists it must be business as usual when the Addicks visit Cardiff City Stadium in midweek.
He said: "I was pleased with how we played up to the sending-off against a team who are really on form. We had to go toe to toe from the first minute and we did that.
"We got the goal and then after the sending-off it can be difficult to play against 10 men but we were absolutely on the money.
"We now have a game against Charlton against, who we gave our poorest performance of the season at The Valley, and we know we will have a tough game against them here.
"We had a record attendance here and I would imagine there is not a ticket to be had for Tuesday, and we will go into the next game in the same vein as this and the same vein as last Tuesday against Barnsley."