The Springboks won 64-0, running riot in the second half at the Olympic Stadium to qualify for the World Cup quarter-finals as Pool B winners having lost their opening game to Japan.
South Africa found themselves embroiled in a maelstrom of negativity following that huge upset but responded, when the pressure was on, by crushing Samoa 46-6, subduing Scotland 34-16 and overwhelming a second-string Eagles team.
"We did not give away a try, you have to win World Cups with defence. One try in last three games, and that was an interception (against Scotland)," Meyer told a news conference.
"I'm proud of the guys, we mauled well and scrummed well. We stuck to our gameplan.
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"That's Springbok rugby, that's power rugby. We need to keep out feet on the ground and stay humble but at stages we played some great rugby."
Meyer was delighted with the continuity after a short turnaround from beating Scotland in Newcastle on Saturday, and that his side had the discipline to shut the door on a U.S. team who kept attacking right to the end.
"I'm happy we scored tries but happy we didn't concede. We weren't sharp in the first half... usually we haven't played a game with three days turnaround. We haven't faced that in our lives.
"The senior guys must get a lot of credit for putting their bodies on the line."
The Springboks will face Wales or Australia in the last eight.
South Africa have lost their last encounters with both. In November last year at the end of their northern hemisphere tour they went down to a 12-6 defeat in Cardiff -- only the second time they have lost to Wales.
They were beaten 24-20 by Australia in Brisbane in July, having victory snatched away by the Wallabies when Tevita Kuridrani scored with the last play of the game.
Asked if he minded which quarter-final opponents the Springboks played, Meyer joked that the only team he did not want to face was Japan.
"They almost cost me my... no, I won't go into that," he said to laughter.
Then, in serious mode, he added: "I said from day one, without sounding arrogant, if we play the way we can, stick to what we are good at, play to our strengths and discipline and a good defence we are good enough to beat any single team."
(Editing by Ed Osmond)
