Meyer and captain Jean de Villiers sought to temper expectations and guard against smugness after the Springboks began the four-nation, southern hemisphere championship with an emphatic 73-13 victory in Johannesburg on Saturday.
"We need to be humble. It was clinical performance that was pleasing but we have to build an innings from there," the coach told a news conference, using a cricketing cliche after a dominant display of rugby.
In Saturday's triumph, South Africa bettered the competition record for the biggest winning margin and their own 16-year-old mark for the most points scored in a match.
They headed off in confident mood on Sunday to the Argentine city of Mendoza, where they play a return match on Saturday.
"Saturday will be war," Meyer said.
"We need to up the tempo there but I have a lot of confidence in this team. The great thing about this team is that we are growing and we had a massive contribution from players off the bench.
"Usually when you make replacements, it (the game) gets loose. When you know you can take your captain off with 20 minutes to go and the performance stays the same, it is awesome. It was one of those days when everything went right."
De Villiers, who scored an intercept try and set up another in a nine-try romp at Soccer City, felt the 60-point winning margin could have been even bigger.
"There were still chances we created that we didn't capitalise on," he said.
"The score was good but we must put things in perspective. There is still a lot of work to do and we need to get better every week."
South Africa were held to a draw by Argentina in Mendoza last year and are expecting a similarly close encounter, even though Saturday's match was surprisingly one-sided.
"I think they'll be a totally different team in Mendoza," De Villiers said. "They'll be hurting after losing (by) such a margin."
South Africa must still play world champions New Zealand and Australia, both home and away, in September and October.