While Meyer said it was the greatest victory of his tenure in charge, Gatland called it his worst defeat as coach.
The truth is that Wales did not deserve to lose a game they dominated for large parts and in which they looked the more accomplished side.
That is small comfort for Gatland, who refused to lay the blame at referee Steve Walsh after the official awarded two penalty tries and issued two yellow cards against his side, at one stage leaving them with 13 men on the field.
"It was probably [the toughest defeat] of my whole coaching career," Gatland told Sky Sports. "It's tough. We played pretty well in the first half and put ourselves under pressure with the two yellow cards but gave us the opportunity."
Wales were within two minutes of the win when fullback Liam Williams' last-ditch tackle on Bok wing Cornal Hendricks was deemed illegal with no use of the arms, leaving Walsh to award a penalty try.
"We're gutted and we didn't deserve that final result. I thought the referee had a good game and did a good job," Gatland said. "In the last 10 minutes they were throwing everything at us and we let Hendricks go through and the penalty try was unfortunate because we got narrow and allowed the winger to get outside us."
Despite the result, Gatland was pleased with the overall performance, a step-up from their timid display in losing the first test 38-16 in Durban last week.
"There was a big improvement on last week. We put South Africa under a lot of pressure and scored some good tries. I'm proud of the effort and performance."
Meyer's mood was much brighter after seeing his side pull off a win having trailed by 13 points going into the last 10 minutes of the game.
"This was my best win yet with the team as these are the matches you coach for," he said.
"We were down and almost out, but the team showed massive character and resolve to pull this one through."
"Wins like this stand out as this is where one's coaching philosophy and team selection are put under massive pressure. We had to dig very deep against a very good team.
"It is always difficult playing a tough team in consecutive weeks and we needed some luck out there today. Credit to Wales, who played very well."
Meyer, who had called for an improvement in execution from his side this weekend, if anything, got the opposite result.
"In Durban we took every opportunity we had and scored. This weekend we did not and nearly paid the price," he said.
"There is not much between the top sides in the world and I am very happy with the final result. It was an awesome match."
(Reporting by Nick Said; editing by Martyn Herman)
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