Argentina moved to the top of the Championship ladder with their first win, 25-18, on New Zealand soil, but Cheika warned, "It's a blockbuster because they're going to be coming with everything.
"It'll be a great lesson for us on how to react in these situations when they'll be coming hard. We've got to bring something as well."
Cheika said after the game that on Argentina's road to the World Cup, achieving some firsts were important because of the boost they gave to confidence.
"Self-belief is a big issue for us to work on. We haven't won a lot of games in the Rugby Championship so getting that mentality right is really important."
It also consolidated the work that was going into achieving winning consistency.
Cheika felt Argentina got better as the game advanced. The All Blacks were making yards on them earlier when trying to go through the middle of the defence.
"We knew we had to win the middle but then in the last 20-25 we started getting off the line, started understanding that you have got to get up there and make those decisions to make the tackles."
He was surprised the scrum was under pressure because it was an area they had been going well. But he thought their substitutes had done well.
"One of the big things we have been trying to work on is the game is not perfect. When it gets difficult, or things go against us, don't worry. That's the time to stand up and rip into it and enjoy the game because that's what rugby's about, being strong in the difficult times.
"That's what I want from this team. They've got the character to do that, they've just got to get used to doing that."
While New Zealand was concerned about some rulings at the breakdown, Cheika felt parity had been achieved in that area because there was not a lot of opportunity for either side to get onto the ball.
Achieving parity with the All Blacks was good for Argentina because it was an area they had been trying to improve.
"The ruck is an important part of the New Zealand game and we wanted to be good there."
Cheika said the time loose forward Pablo Matera had spent with the Crusaders in Super Rugby had made a 'huge' mark on him.
"He came here to learn more about rugby…and he's come back a heap better player mentally and technically so it will have been bittersweet for him."
He was proud of his Christchurch connection, but he would also be proud of the win.
Captain Julián Montoya said he was proud of the win, but they needed to work on a lot to get better.
Montoya paid tribute to former Kiwis league captain David Kidwell for his work on the side's defence.
"It was a pleasure to work with him, and he had made a difference for the side."