Tom Maher's side pushed the reigning world and Olympic champions before Auriemma introduced his big players, including Maya Moore and Lindsay Whelan, to gain control of the game, eventually running out 88-63 winners.
But the USA coach believes that if Team GB perform to their best and continue to improve, they will be able to pull off shocks in one-off games at London.
"There's a tremendous improvement in Great Britain," said Auriemma, who took over the team in 2009.
"We knew they were going to be good as we saw the victory they had against a really good France team, so I'm not surprised by some of the things they were able to do.
"From my experience as an assistant at the Olympics, it's all about what match-ups you get and what happens that one individual night.
"You don't have to win a best out of three or five series - it's just that night. If France and Russia played Great Britain in a best of seven series, then maybe they win that series.
"But on a one night, Great Britain nearly beat Russia, and they beat the French. I think they've proven to themselves that they can compete with the best teams in the world."
The American coach admitted he was taken aback by his side's sluggish start to the showpiece event at the Manchester Arena, but was pleased that he had the options to make changes.
Great Britain led 21-10 at one point in the first quarter, but the introduction of Moore, Whelan and Angel McCoughtry swung things back in the Americans' favour.
"I wasn't surprised by Great Britain's start, but I was surprised by ours," he said.
"When you're playing big games and you're the United States, you always expect the other team to be more ready than they ever will be.
"We're blessed to have the depth that allows us to bring in that second group and it changed the whole complexion of the game with Maya, Lindsay and Angel. They were the major difference in the game.
"It might have been the best thing that happened to us to get down by 11 because sometimes when you're the United States, you're constantly playing ahead and you never get an opportunity to play from behind and see how you're going to respond."
Meanwhile, player of the match Moore has predicted a bright future for lead Great Britain player Jo Leedham after she turned in a strong performance, netting 21 points.
Moore said: "She's tough, plays with a lot of confidence and she plays hard the whole game.
"She looks like someone who knows how to play and anytime you know how to play basketball and have talent for being a shooter, you have a shot anywhere.
"You could tell she was their leader and their go-to for a score and I had a lot of respect for how she played today."
