Paulinho's last-gasp winner downed the Bluebirds, who had a goal disallowed on the stroke of half-time when Ben Turner's header from a corner was discounted after referee Mark Clattenburg ruled Spurs keeper Hugo Lloris had been impeded by Aron Gunnarsson.
Early on, Lloris appeared to have handled outside the box when he robbed the ball from Fraizer Campbell's feet after a poor Kyle Naughton back-pass but he was not sent-off.
Mackay told Sky Sports: "I suppose everybody will look at that (the Lloris handball), I'm more disappointed that Frazier never stuck it away.
"He's a very good finisher, he got onto it really well, read it really well, and he's disappointed himself that he never finished that.
"And we're disappointed about the disallowed goal and I think the referee will look at that tonight and Hugo Lloris will look at that tonight and Hugo will think he is very lucky.
"He was the one who was holding onto Aron Gunnarsson and it can be seen clear when you look at the replay."
At the time there was confusion over whether or not the goal was disallowed for a Turner push on Michael Dawson as he went for the header, but Mackay said: "I cleared that up with the fourth official, I asked the fourth official and he was very clear it Gunnarsson on the goalkeeper which again, when you look at it back, it's quite extraordinary."
Mackay also praised David Marshall's display, but felt the defeat shows the challenge his side face in the top-flight.
"I don't think what you deserve comes into it, that's the harsh reality, they were clinical in the last minute and we weren't in the first minutes when we were through on goal," he said.
"David is a top goalkeeper, I think their goalkeeper cost £9million and I look at my keeper today and see him step up. He was the best in the Championship and he is in the Premier League, back in the Scotland squad and he has looked so comfortable in the games we have played against some top teams."