The former Wallabies coach was unapologetic about his enthusiastic celebrations of the Pumas' 25-18 victory at Christchurch Stadium, which put them top of the Rugby Championship after three rounds.
"For those Argentina boys, that's historic for them and I want them to enjoy it," he said. "It's a first for me too, I've never won a test match in New Zealand.
"I'm looking to grow the team, particularly towards the World Cup, and what's important for us now is getting ready for next week.
"Because they're going to come back with every piece of artillery they've got and we've got to find a way to handle that and give something back."
Cheika, who has now overseen four wins from six matches in his first season in charge of the Pumas, said he had not held back in his pre-match and halftime team talks.
"They are guys who haven't won a lot of Rugby Championship games and maybe not a lot of self belief," he said.
"So you've got to bring (emotion) as well as the technical to make them believe in themselves.
"We knew we had to bring intensity, we knew they had a bit of pressure on them so we had to try and build on that, and then just take it from there and see where the game lands."
Like their first ever victory over the All Blacks in Sydney two years ago when Cheika was a consultant with the team, Saturday's victory was built on an incredible defensive effort.
Cheika paid credit to his new defensive coach Dave Kidwell for what he had brought to the team.
Kidwell was born in Christchurch and has a mural in the city honouring his days as a player and coach with the New Zealand rugby league team.
"It was awesome, the guys have been building week by week and this is just the result of the hard work they've been doing," Kidwell said.
"It's all about the connection in the line and moving as one, making sure we're tackling well. It's pretty simple."
While Kidwell confessed to having some mixed feelings as a "Maori boy at heart", there were no such conflicts for Argentina's Pablo Matera, who played the last Super Rugby season for the Christchurch-based Canterbury Crusaders.
"It's like a dream come true," said the inspirational number eight.
"Being able to beat the All Blacks for the first time in our history on New Zealand ground is very special and to do it in Christchurch, a place that I love, a place that I feel like home, is even more special."
For Ian Foster, the head coach of New Zealand, this result only piles the pressure on him after a dismal couple of months.
"Congratulations to Argentina, they kept true to how they wanted to play, they really frustrated us," he added.
"We didn't get what we wanted at the breakdown. We had large periods of dominance in our set piece but that didn't go well at the end.
"But overall they got away with some stuff at the breakdown and we weren't able to deal with it."
Foster has endured a torrent of criticism this year after New Zealand lost their July series to Ireland and their Rugby Championship opener in South Africa.
It was only after the victory in Johannesburg two weeks ago that he was confirmed in his job through to next year's World Cup.
The reigning tournament champions have the chance to make immediate amends when they face the Pumas in Hamilton next week and Foster said there were some positives to take out of Saturday's match.
"We've got to look at the dominance we got in the first two thirds of the game, particularly at lineout and scrum time," he said.
"But just a little bit of discipline and some frustration and that's a key thing they play on."