Michael Bostwick and Dwight Gayle fired Posh into a two-goal lead before Rudy Gestede netted a late consolation for the Welsh pacesetters.
Cardiff had gone into the match on the back of 10 straight home wins and Mackay said: "There are no easy games in this division and everyone can beat everyone - but we are disappointed to lose.
"On another day Heidar (Helguson) could have scored five. We had 20 attempts on goal, did everything but score and weren't clinical and that wasn't good enough.
"We were beaten and can play much better. We want to be as consistent as possible and the league table shows that but we have to work hard every week.
"We were bound to lose at home at some point but full credit to Peterborough. They deserved the win.
"Darren Ferguson always has a good football team and if they keep playing like that they won't have an issue this season."