"We could have lost the game, without a doubt, but we didn't. The guys will hopefully be better for the win."
Banahan's 69th minute try saved England's blushes in wet and blustery conditions at Twickenham, where 78,000 fans had hoped for an improved display on last week's defeat to Australia.
However, many of them were sent home disappointed, as an Argentine side missing five first-choice players and including four amateurs in their starting line-up pushed Johnson's side all the way.
And Johnson, who now has six wins from 13 games since taking charge in 2008, admitted his side had dug themselves into a hole from which they were lucky to get out of.
Moody unimpressed by England win
"Once you get yourself into that sort of game and guys are getting nervous and have made mistakes, and there's pressure building on the scoreboard and on the clock, it just becomes a matter of trying to win however you can win and we got the try to go ahead and we held out," said Johnson.
"You have errors in decision-making which will always happen, guys aren't perfect, and you get nerves, guys know how important it is, and once you get in that cycle it can go through a team.
"There were a few nerves around earlier on and we probably kicked away a bit of ball we could have played with, and we didn't handle their high ball at times.
"And when we did build momentum it was quickly snuffed out with an error. They were competitive round the breakdown and made it difficult at times and I thought the referee might have given us a little bit more in that area.
"The good thing is we came out of it, guys made mistakes and bounced back with good plays and didn't let their heads go down.
"In a game like that today, in wet, windy, blustery conditions, it's about execution, which we didn't do well enough at times, I can't defend some of the things that happened on the field.
"But it's about beating Argentina and we did that. It's difficult to tell [whether England are better than when Johnson took over] after a game like that, with the changes we've had in the squad.
"I said to the players, we can say a hundred things about the game, but ultimately we won it."
England captain Steve Borthwick said his side had done "really well" in the second half, and also blamed the conditions for the amount of mistakes.
"We managed to lift the speed of the game [in the second half] and got rewarded in the latter quarter. Great credit to the boys for the way we stuck at it," said the Saracens lock.
"We knew it would be a tough, tight affair with the conditions. We knew there would be mistakes and spoke about it at half-time, about lifting the pace.
Argentina encouraged by performance
"We felt we'd somehow get the breakthrough. We could have played better today but we believe in what we are trying to do here.
"There are things we could have done much better but credit Argentina, they have world-class players, especially in their pack. We respect that fact."
Lewis Moody, who was England's man of the match: "I don't think we're satisfied with the performance but we're certainly satisfied with the win.
"We were certainly a bit disappointed at half-time with the way things were going but we came out and lifted the tempo.
"Unforced errors kept allowing them back into the game but we worked hard. The rain was lashing down, we had to dig deep.
"We came out with a game-plan dictated by the weather. We felt they never offered much in attack, they lived off our turnovers, but the most important thing was to get a win."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.