Both Wayne Rooney and Gary Medel could have conceivably been sent off, with the United striker kicking out at Jordon Mutch in the first half and the Cardiff defender raising his hands to the face of Marouane Fellaini in the second.
Referee Neil Swarbrick opted not to dismiss both players - and Rooney went on to score the opening goal, via a deflection from Medel, and set up Patrice Evra's headed goal which put the visitors 2-1 ahead.
Substitute Kim Bo-kyung headed home a dramatic equaliser in stoppage time, with Fraizer Campbell netting the best goal of the game on 33 minutes to cancel out Rooney's 15th-minute opener.
While Mackay admits Medel could have been dismissed, he also believes United midfielder Fellaini needs to be careful with the way he marks.
Asked about Medel, Mackay told Sky Sports: "He could (have been sent off) but then I also look at Fellaini and doing what he does normally and putting his head on someone else's face, and that's for me a sending off. So I think that's something that needs to be looked at as well.
"Having seen the way Fellaini marked and used his arms at times in the game, not all the times but at certain points, but more so putting his head into someone's face, I think that also justifies having a look at.
"But overall I'm happy that both teams deserved to have 11 men on the pitch. They didn't deserve to have any men off and neither did we."
Evra's goal looked set to earn United a valuable three-point haul from the trip to south Wales, but Kim climbed off the bench to earn his side a point.
Mackay added: "I think we played really well today. In terms of chances I
thought we created a lot, we passed the ball really well.
"It's probably the most complete first-half performance we've had this season. We were playing the champions so I'm delighted."