If he was a little greyer around the temples by the final whistle, Johnson was at least able to celebrate what he called "a fantastic win" in the circumstances.
Ben Youngs came on to score the only try of the match after 68 minutes and Jonny Wilkinson's conversion nudged England into the lead for the first time.
England were second best for much of a brutal Test match and they were penalised heavily by referee Bryce Lawrence, which led to the Pumas leading 9-3 early in the second half.
Argentina could have been out of sight but their kickers missed six penalty shots and a drop-goal.
Wilkinson also had a shocking day with the boot, sending five penalty attempts wide including four in the second half as England sought a way back into the game.
But it was Youngs, making his first appearance since undergoing knee surgery in the summer, who provided England's 'get out of jail free card'.
"We said before the tournament that World Cup games are about finding a way to win in difficult circumstances against difficult teams," said Johnson.
"Clearly it could be a lot better but we found a way to win the game. All the players are frustrated but in the circumstances that is a good win, a fantastic win."
England knew just how dangerous Argentina would be. The Pumas stunned France in the opening game of the last World Cup and went on to finish third in the tournament.
"In 2007, France would have bitten your arm off to win that game," said Johnson.
"They are a team that will keep possession and squeeze penalties. It makes it difficult but we got over the line.
"These games are black and white and we found a way to win. We could easily have lost that game and we didn't."
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