Mackay said: "We were below par in the last two games, but it had zero to do with being in the cup final.
"It was good to get back to winning ways and the way we went about our business. We looked more like the team that we've been since the start of the season. We got after our opponents and won a lot of second balls.
"I'm delighted with the result and performance and the amount of chances we created.
"It's tight at the top, other results have gone our way and we are back in the mix."
Peterborough were the better side in the opening 34 minutes as Paul Taylor and then Grant McCann threatened.
But the home team did not look back once Whittingham broke the deadlock when his corner was bizarrely diverted in by Peterborough goalkeeper Joe Lewis.
Four minutes later, Cardiff doubled their advantage as Gestede rose highest from Don Cowie's corner to power a header past Lewis.
Then Slovenian midfielder Vuckic, making his home debut following his loan move from Newcastle, slotted home from close-range after the visitors failed to clear Aron Gunnarsson's long-throw.
Taylor grabbed a consolation for the shellshocked visitors deep in injury-time, but it was a case of too little, too late.
Peterborough manager Darren Ferguson said: "We were in complete control of the game but it was a mad six minutes. We were three-nil down and it was hard to take.
"Joe made a mistake for the first, we've lost a man for the second and the third is an appalling goal to concede.
"Cardiff is a difficult place to come to but they showed us a lot of respect by matching us up with a diamond formation.
"But we didn't have the right concentration levels which top players have. The second half looked like it was a comfortable night for Cardiff but it's easy to play well when you are three up.
"At 0-0 it's a different game. We have to learn from it quickly."