Hooker Bismarck du Plessis received his marching orders in the second half when he received a second yellow card for elbowing All Black loose forward Liam Messam in the throat.
However, he was unjustly given a yellow card in the first half when he tackled New Zealand flyhalf Dan Carter.
The intensely physical battle erupted into an all-in brawl in the 15th minute when the incident occurred.
It took referee Romain Poite a full minute to restore order, and when the dust settled the injured Carter was out of the game and Du Plessis received 10 minutes in the sin-bin.
But Meyer refused to blame the cards for the loss and said he had no excuses.
"The ref is always right," Meyer told AFP.
"If you start making excuses for your team then they start to make excuses. There were a lot of things that weren't good enough even when we had 15 men on the field."
The All Blacks themselves finished with only 13-men with two yellow cards in the final 10 minutes when captain Kieran Read was dismissed for a lineout foul and Ma'a Nonu was sent from the field for a shoulder charge.
Their coach Steve Hansen said Du Plessis may have been "unlucky" with his first yellow card but overall he had no complaints about the refereeing.
"In an intense battle like that your going to get moments," he said.
"You don't like seeing it but it happens and you pay the price for being ill disciplined. We paid it twice."
Tries: Kieran Read (2), Brodie Retallick, Sam Cane
Conversions: Daniel Carter, Beauden Barrett (2)
Tries: Bismarck du Plessis, Pat Lambie
Conversion: Morné Steyn
15 Israel Dagg, 14 Ben Smith, 13 Conrad Smith, 12 Ma'a Nonu, 11 Julian Savea, 10 Daniel Carter, 9 Aaron Smith, 8 Kieran Read (captain), 7 Sam Cane, 6 Liam Messam, 5 Sam Whitelock, 4 Brodie Retallick, 3 Owen Franks, 2 Dane Coles, 1 Tony Woodcock
Substitutes: 16 Keven Mealamu, 17 Wyatt Crockett, 18 Charlie Faumuina, 19 Steven Luatua, 20 Matt Todd, 21 Tawera Kerr-Barlow, 22 Beauden Barrett, 23 Charles Piutau
15 Zane Kirchner, 14 Willie le Roux, 13 JJ Engelbrecht, 12 Jean de Villiers (captain), 11 Bryan Habana, 10 Morné Steyn, 9 Ruan Pienaar, 8 Duane Vermeulen, 7 Willem Alberts, 6 Francois Louw, 5 Flip van der Merwe, 4 Eben Etzebeth, 3 Jannie du Plessis, 2 Bismarck du Plessis, 1 Tendai Mtawarira
Substitutes: 16 Adriaan Strauss , 17 Gurthrö Steenkamp, 18 Coenie Oosthuizen, 19 Juandré Kruger, 20 Siya Kolisi, 21 Jano Vermaak, 22 Pat Lambie, 23 Jan Serfontein