The Bluebirds felt they had twice come out on the wrong end of decisions by the officials in the 1-0 defeat.
The first came when Lloris appeared to handle outside his area as Campbell attempted to round him, although replays suggested it was a very tight call.
The second saw Turner's header from a corner chalked off after Aron Gunnarsson was adjudged to have impeded Lloris.
Andre Villas-Boas felt the officials had got it right on both counts, but Mackay said: "Hugo Lloris will see it back and realise he is a lucky man and the referee will be disappointed in his decision," said the Scot.
"If you look at it again, it is Lloris who has his hand on Gunnarsson and then completely misses the track of the ball so for me it is a clear goal.
"The incident with Fraizer is one people will look at whether it was out or in, but we had a one-on-one and Fraizer is invariably brilliant at those, and he is more disappointed he did not skip by him. Whether it was a foul or not is open to question.
"We had some real good chances, but it's about being clinical."
Mackay also praised 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 B£9million and I look at my keeper 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."
Spurs dominated large passages of the game at Cardiff City Stadium, and registered 29 shots to Cardiff's six, but were in danger of failing to capitalise as they found home goalkeeper David Marshall in fine form.
The Scotland international made a string of saves from Roberto Soldado, Christian Eriksen, Paulinho and Gylfi Sigurdsson, and even when former Swansea man Sigurdsson did beat Marshall, he was denied by the crossbar.
But Paulinho finally broke the deadlock as he backheeled in Erik Lamela's pass from close range in the 92nd minute for his first league goal for the club.