The All Blacks claimed a 33-16 victory over the Springboks in the opener of the four-match series in Johannesburg on Saturday and moved top of the World Rugby rankings.
World champions South Africa had numerous entries into the New Zealand 22 and created chances to score, but a mixture of errors under pressure and some excellent defence from the visitors kept them to one try at Ellis Park.
The Springboks also had two players sent to the sin-bin in the final 11 minutes, Reinach being one of them, and played out most of the remainder of the game with 13 men.
"They put us under pressure and made us do things that led to my yellow card, but it’s now up to us to work on that and see how we can defend certain things better or make a better plans," Reinach told reporters.
"The review after a loss is never good, but it’s learnings, and as long as we take the lessons and grow as a team, we will be in a good place."
Both Reinach and the man he replaced at scrumhalf, Grant Williams, had a difficult evening and were put under pressure from the visitors.
"I don’t think they targeted us as individuals as number nines, they went after our breakdowns quite hard and tried to slow down the ball with throwing their legs and other things," said Reinach.
The All Blacks are embarking upon their first full tour of South Africa since 1996! Marketed as the 'Greatest Rivalry' series, the winner will come out not only with the bragging rights but World Rugby's number one ranking. Keep up to date throughout August and September with news, previews and more.
All tour fixtures | All tour results | Rugby match previews | Rugby news
"We felt the pressure and we knew we had to get the ball out somehow, and we have to work out ways around it. When we train, we try to emulate that, and try to figure out ways in which we can improve."
The third match is back in Johannesburg on September 5 before the series wraps up a week later in Baltimore in the United States.