The Boks went down 33-16 at 10bet Ellis Park, and will have Sunday off to recover from the physically demanding clash, before returning to the training field on Monday to begin their preparations for the second encounter between the sides at the DHL Stadium in Cape Town next Saturday.
"We'll obviously watch the game again and work through it," Kriel told the media afterwards.
"We have another whole week to prepare, and we'll do what we need to do. We're a team that finds solutions, and we'll be up for it next week."
The experienced centre, who earned his 91st Test cap, reiterated Springbok coach Rassie Erasmus' sentiments after the match that at top international level, you have to convert your opportunities into points.
"In Test match rugby, if you don't convert and take your opportunities and other teams do, the scoreboard is normally not in your favour and we clearly had to be more clinical," said Kriel.
"The All Blacks were when they got their chances, and at the highest level between the two best teams in the world, that's what happens.
"There are very small margins for error in a Test match of this magnitude and on an occasion like this, so we'll have to be better there, and we are looking forward to the challenge next week."
With the Bok coaches forced to make several positional changes during the game due to a series of occurrences throughout the match, Kriel, who moved to wing, said they do plan for situations like that.
"In big games like this you have to be able to adapt," he said.
"It doesn't normally happen a lot, but when it does, I think we reacted pretty well. I just don't think we were as accurate as we wanted to be on the night, and New Zealand put us under a lot of pressure."
The Springboks will remain in Johannesburg until Wednesday and travel to Cape Town on Thursday. They will then return to Johannesburg for the third match between the sides at the FNB Stadium near Soweto before travelling to the USA for the closing game of the competition in Baltimore.
Rassie Erasmus says the anticipated wet weather, and Handre Pollard's familiarity with the Cape conditions, prompted him to select the two-time World Cup winner for Saturday's All Blacks rematch.
Lions head coach Ivan van Rooyen admitted his side are a little undercooked for their Rugby's Greatest Rivalry tour match against the All Blacks but believes the occasion will help elevate their performance.
Rassie Erasmus has taken responsibility for a number of tactical errors that cost the Springboks dearly in the opening Test of Rugby's Greatest Rivalry.
Springboks Pieter-Steph du Toit and Ox Nche both earn career milestones in the second Test of Rugby's Greatest Rivalry against the All Blacks in Cape Town this Saturday.
