Argentina had a man advantage for most of the game after a red card for England flanker Tom Curry, but never looked in control as fly half George Ford kicked 27 points to guide his side to victory.
"Pretty much everything that could go wrong did go wrong," Cheika told reporters. "England managed the game very well, it was stop-start, which was how they wanted it. Ford played the cards nicely in this scenario.
"The pitch here is also smaller, only 95 metres so you can take a shot from further out.
"Full credit to them, they did not let us get flow into our game. Ford was excellent, not just his kicks at poles but also in general play."
Argentina face Samoa on Friday in what is now a must-win contest in Pool D.
"The world is not over," Cheika said. "We still have work to do to qualify. Our players will take a lot from this experience. We have many first-timers in World Cup games and they will take a lesson of how we need to be ready when the whistle blows."
Argentina captain Julian Montoya admitted his side were below par.
"The attitude of the team to go until the last minute and score a try is important," he said. "We need to figure out why we didn’t do that for the 80 minutes. We are not at the standard we want to be at.
"It’s a bad thing to happen but it’s better that it happened in the first game. We can learn from it."
